DEPARTMENT OF BIOTECHNOLOGY

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1 DEPARTMENT OF BIOTECHNOLOGY Faculty Name : Mr. R. Gnanasekaran Faculty Code : HTS 1342 Subject Name Subject Code Year & Semester : Chemical Reaction Engineering : BT6604 : III & VI VTHT 1

2 DEPARTMENT OF BIOTECHNOLOGY COURSE DETAILS Faculty Name : Mr. R. Gnanasekeran Faculty Code: HTS 1342 Subject Name: Chemical Reaction Engineering Department: Biotechnology Subject Code: BT6604 Year & Semester: III & VI COURSE OUTCOMES On completion of this course, the students will be able to CO No C316.1 Course Outcomes Understand how an experimental investigation carried out in order to determine the rate equations. Knowledge Level C316.2 Describeabout material and energy balance for ideal flow reactor K2 C316.3 Understand about the RTD studies for non ideal flow reactors K2 Describe about the usage of standard statistical method to establish C316.4 quantitative method K2 C316.5 Understand about the design of reactors for bio based product K2 K2 Mapping of Course Outcomes with Program Outcomes and Program Specific Outcomes BT6604 PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3 PSO4 C C C C C BT6604 PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3 PSO4 C K1 Remember; K2 Understand; K3 Apply; K4 Analyse; K5 Evaluate; K6 - Create Mapping Relevancy: 1: Slight (Low) 2: Moderate (Medium) 3 Substantial (High) - : No correlation VTHT 2

3 UNIT-I - SCOPE OF CHEMICAL KINETICS & CHEMICAL REACTION ENGINEERING PART-A QUESTIONS & ANSWERS CO Distinguish between homogeneous and heterogeneous reactions. (May2017) Homogeneous reactions: A reaction is homogeneous if it takes place in one phase alone. Most gas-phase reactions and fast reactions such as burning of a flame are non-catalytic type. Most liquid phase reactions, reactions in colloidal systems, and enzyme & microbial reactions are catalytic type. Heterogeneous reactions: A reaction is heterogeneous if it requires the presence of at least two phases to proceed at the rate it does. Burning of coal, roasting of ores, attack of solids by acids, and gas-liquid absorption with reaction are non-catalytic type. Ammonia synthesis, oxidation of ammonia to produce nitric acid, cracking of crude oil, and oxidation of SO 2 to SO 3 are catalytic type. 2. Define the term Rate of reaction. (May 2012) The rate of reaction is defined as the rate of change in number of moles of any component i' due to chemical reaction per unit volume of the reacting fluid. It is given by the expression, r i = (1/V) (dn i/dt) = [moles of i formed] / [(volume of fluid) (time)] Significance: Negative sign for reactants & positive sign for products. 3. What are the variables affect the rate of reaction? (NOV 09) Many variables affect the rate of reaction of a chemical reaction. In homogeneous systems the temperature, pressure, and composition are obvious variables. In heterogeneous systems, material may have to move from phase to phase during reaction; hence, the rate of mass transfer can be important. In addition, the rate of heat transfer may also become a factor. 4. What are single and multiple reactions? Single reaction: When a single stoichiometric equation and single rate equation are chosen to represent the progress of the reaction, then it is said to be single reaction. Multiple reactions: When more than one stoichiometric equation is chosen to represent the observed changes, then more than one kinetic expression is needed to follow the changing composition of all the reaction components, it is said to be multiple reactions. Multiple reactions may be classified as; Series reactions, Parallel reactions, and Series-Parallel reactions. 5. Discuss the reaction rate of homogeneous reactions. Suppose a single-phase reaction aa + b B r R + s S. The most useful measure of reaction rate for reactant A is then -r A = - (1/V) (dn A/dt) = [Amount of A disappearing] / [(Volume) (Time)], [mol/m 3 -s] Where (-r A) is the rate of disappearance of A and it is the intensive measure; Minus sign means disappearance.in addition, rates of reaction of all materials are related by (-r A) / a = (-r B) / b = r R/ r = r S/ s. 6. Define the terms Molecularity& Order of an elementary reaction. (May 2017) The number of molecules involved in the reaction is called molecularity. The sum of the powers of the concentration terms involved in the rate equation of a reaction is called Order of that reaction. 7. Differentiate elementary and non-elementary reactions. (May2011, 2012,2014 & 2015) The reactions in which the rate equation corresponds to a stoichiometric equation are called elementary reaction. The reactions in which there is no correspondence between stoichiometry and rate equation are known as Non-elementary reaction. 8. With suitable example, show the representation of an elementary reaction in terms of partial pressure. For isothermal (elementary) gas reactions where the number of moles of material changes during reaction, the relation between the total pressure of the system to the changing concentration or partial pressure of any of the reaction component is aa + b B +... r R + s S + For the component A, p A = C A R T = p Ao [(a/ n) ( - o)] VTHT 3

4 For the component R, p R = C R R T = p Ro + [(r/ n) ( - o)] And the rate of the reaction, for any component i', is given by r i = (1/RT) (dp i/dt) 9. How will test the kinetic models that involve a sequence of elementary reaction? In testing the kinetic models that involve a sequence of elementary reaction, we hypothesize the existence of two types of intermediates; Type-I: An unseen and unmeasured intermediate X usually present at such small concentration that its rate of change in the mixture can be taken to be zero. Thus, we have [X] is small and d[x]/dt = 0. This is called the steady-state approximation. Type-II: Where a homogeneous catalyst of initial concentration C o is present in two forms, either as free catalyst C or combined in an appreciable extent to form theintermediate X, an accounting for the catalyst gives [C o] = [C] + [X]. We then also Assume that either (dx/dt) = 0 orthat the intermediate is in equilibrium with its reactants. Using the above two types of approach, we can test the kinetic model or search a good mechanism; Trial and error procedure is involved in searching for a good mechanism. 10. For the elementary reversible reaction, 2A R + S, Derive the relation between equilibrium constant K c, k 1 and k 2. 2 For the given, the rate of reaction is -r A = k 1 C A - k 2 C R C S. 2 At equilibrium, -r A = 0. Then, k 1 C A - k 2 C R C S = 0 (or) K c = k 1 / k 2 = (C R C S) / C A For a reactant A (initial concentration C Ao), its C A varies according to (1/C A) (1/C Ao) = k t. where t is time and k is kinetic constant. Derive an expression for the rate of reaction. The given expression can be rearranged as (1/C A) = k t + (1/C Ao) -1-1 or C A = k t + C Ao Differentiating the above expression on both sides, we have -dc A/C 2 A = k dt + 0 or -(dc A/dt) 2 = k C A or -r A, rate of the reaction = -(dc A/dt) 2 = k C A 12. Differentiate between differential and integral method of analysis of batch rector data. Integral method of analysis: It is simple to work and is recommended when testing specific mechanisms, or relatively simple rate expression. (elementary reactions) Order obtained is accurate. It has a disadvantage that it fails to test the rate expression involving fractional orders and involves multi-stage analysis in testing the rate form. Differential method of analysis: Single stage analysis, tests any mechanism or rate form. It is the best analysis for fractional order reactions. It can be used to develop or build a rate equation to fit the data. It has a disadvantage that it requires more accurate or large amounts of data to evaluate (dc i / dt), which is the slope of the curve C i versus t, at different intervals of t and it is difficult to work also. 13. A reaction has the stoichiometric equation A + B 2R. What is the order of reaction? By considering the given reaction as elementary, we can write the rate of reaction as, -r A = k C A C B. Where k is the reaction rate constant. From the definition of order of reaction sum of the powers of the concentration terms involved in the rate equation, we have Order, n = = A certain reaction has a rate given by -r A = 0.005C A2, mol/cm 3 -min. If the concentration is to be expressed in mol/liter and time in hours, what would be the value and units of the rate constant? If the concentration is to be expressed in mol/liter and time in hours, the given rate 2 expression becomes -r A = 0.005C A x 60 x 10-3 mol/lit-hr = C A2 mol/lit-hr Then the value and the unit of rate constant, k = lit/mol-hr 15. For a gas reaction at 400K, the rate is reported as -dp A/dt = 3.66 p A2, atm/hr. a) What are the units of the rate constant? b) What is the value of rate constant for the reaction if the rate equation is expressed as -r A = - (1/ V) dn A/dt = kc A2, mol/liter-hr Answer: (a) The unit for rate constant is k = 3.66 = - (dp A/dt) 2 / p A = (atm/hr) / (atm) 2 = 1/atm-hr or atm -1 hr -1 VTHT 4

5 (b) We know, p A= C A R T or dp A = (RT) dc A. Then, the given expression becomes - (RT) dc A/dt = 3.66 (C A R T) 2 or - dc A/dt 2 = (3.66 R T)C A or -r A = - (1/ V) dn A/dt = - dc A/dt = (3.66 R T)C A2. On comparing, we get k = 3.66 R T = 3.66 ( ) (400) = lit/mol-hr 16. On doubling the concentration of a reactant the rate of reaction triples. Find the reaction order. n We know, the general rate of reaction is -r A = k C A For the given statement, On doubling the concentration of a reactant the rate of reaction triples, the above rate can be written as 3 (-r A) = k (2C A) n On combining the above rate expressions, we get 3 = 2 n or n = log (3) / log (2) = Differentiate constant volume and variable volume methods of analysis of reactors. Constant volume method: It refers to the volume of reaction mixture, and not the volume of reactor. It actually means a constant density reaction system, that is, the composition of reaction mixture is constant. Most of the liquid phase as well as gas phase reactions occurring in a constant volume bomb fall in this class. In a constant volume system, the measure of reaction rate of component i (reactant or product) becomes r i = (1 / V) (dn i/ dt) = dc i / dt. Conversion of reactant A in this method is given by X A = 1 (C A/C Ao). Variable volume method: It actually means the composition of reaction mixture varies with time by the presence of inerts. Gas phase reactions involving the presence of inerts or of impure reactants occurring in a reactor fall in this class. The measure of reaction rate of component i (reactant or product), in this method, becomes r i = (C io / i) [d (ln V)/ dt). In variable volume system, the fractional change in volume of the system between the initial and final stage of the reaction will be accounted. Thus, conversion of reactant A becomes X A = [1 (C A/C Ao)] / [1 + A (C A/C Ao)]. 18. What is a zero order reaction? (Dec 2015) When the rate of the reaction is independent of the concentration of the reactants, it is called as Zero order reaction. Example: Decomposition of HI 19. What is a pseudo first order reaction? Give an Example. A second order rate equation which follows the first order rate equation is defined as pseudo First order reaction. Example: Ester hydrolysis. CH 3 COO C 2 H 5 + H 2O CH 3COOH + C 2H 5OH (A) (B) (C) (D) When C BO >>C Ao,Concentration of H 2O is very large, - r A = - dc A/dt =k C A. 20. Explain bimolecular reactions with examples. An irreversible bimolecular-type second-order reaction may fall on two categories; (1) The reaction A + B Products with corresponding rate equation -r A = - (dc A/dt) = - (dc B/dt) = k C A C B Here the amounts of A and B that have reacted at any time t are equal. (2) The reaction 2A Products with corresponding rate equation -r A = - (dc A/dt) = k C A 2 Here in practice that the reactant ratios either equal to or widely different from the stoichiometric ratio. 21. Explain third order reaction with example. An irreversible trimolecular-type third-order reaction may fall on two categories; (1) The reaction A + B + D Products with corresponding rate equation -r A = - (dc A/dt) = k C A C B C D. If C Do is much greater than both C Ao and C Bo, the reaction becomes second order. (2) The reaction A + 2B Products with corresponding rate equation -r A = - (dc A/dt) = k C A C B Write the empirical rate equation of n th order. The empirical rate equation of n th order, -r A = - dc A/dt = k C A n (constant volume). Separating the variables and integrating, we get C A 1-n - C Ao 1-n = (n - 1) k t. Case i) n>1, C Ao 1-n = (1 - n) k t. The slope is (1 - n) VTHT 5

6 k is negative Or the time decreases. 1-n Case ii) n<1, C Ao = (1 - n) k t. The slope is (1 - n), k is positive. The rate of the reaction predicts that the reaction will drop to zero at some infinite time which is completion of the reaction (C A = 0). 23. What are autocatalytic Reactions? A reaction in which one of the products of reaction acts as a catalyst is called autocatalytic reaction. Example: A+R R+R 24. Write Arrhenius Law. ( May 2013) The temperature dependency on the reaction rate constant is given by Arrhenius Law. That is, k = k o e -E/RT, Where k = rate constant, k 0 = frequency factor, E = Activation energy, It is the excess energy of the reactants required to dissociate into products. 25. Define Half-life of the reaction. The half life of the reaction t 1/2 is defined as the time needed for the concentration of reactants to drop to one half of its original value. 26. Define Fractional Conversion X A. Fractional conversion of a reactant A is defined as fractional reactant converted into product at any time. It is given by the equation, X A = (N AO N A) / N AO Where N AO is the initial no. of moles of reactant A at t = 0. N A is the remaining no. of moles of reactant at any time t in the reaction. 27. Half-life of a first order reaction A B is 10 min. What percent of A remains after 60 min? We know, the performance equation of a first order reaction taking place in the batch reactor asln(1- X A) = k t Given, at t = 10 min X A = 0.5 (Half-life). Then, from the above equation, we get k = Thus, at t = 60 min, we getremaining A, (1- X A) = exp (-k t) = exp ( * 60) = or 1.56% 28. Define the reaction rate for catalytic reaction. (Dec 2012) Catalytic reactions are typical chemical reactions.i.e. the reaction rate depends on the frequency of contact of the reactants in the rate-determining step. Usually, the catalyst participates in this slowest step, and rates are limited by amount of catalyst and its "activity". 29. Define Chain reaction. (May 2014) A chemical reaction or other process in which the products themselves promote or spread the reaction. the self-sustaining fission reaction spread by neutrons which occurs in nuclear reactors and bombs. a series of events, each caused by the previous one. 30. What is Ea? Find Ea on this reaction A 3R. (May 15) Ea is the fractional change in the volume of the reaction system between no conversion and complete conversion of reactant A. Ea for A 3R: One mole of reactant on complete conversion yields three moles of product. Basis: 1 mole of A From the reaction, 1 mole A= 3 mole R Moles of R formed on complete conversion of A = (3/1)*1 = 3 mole Initial total moles = Total moles at no conversion = 1 mole A Total moles on complete conversion = 3 mole of R = 3 mole Ea = (3-1)/1 = 2 Answer: Ea = Define Activation Energy. (Dec 2015) Activation energy is a term used to describe the minimum energy which must be available to a chemical system with potential reactants to result in a chemical reaction. VTHT 6

7 Activation energy may also be defined as the minimum energy required to start a chemical reaction. The activation energy of a reaction is usually denoted by Ea and given in units ofkilojoules per mole (kj/mol) or kilocalories per mole (kcal/mol). 32. Write the units of rate constant. (May 16) The units of the rate constant depend on the global order of reaction:[2] If concentration is measured in units of mol L 1 (sometimes abbreviated as M), then For order (m + n), the rate coefficient has units of mol1 (m+n 1 ) L(m+n) 1 s For order zero, the rate coefficient has units of mol L 1 s 1 (or M s 1 ) For order one, the rate coefficient has units of s 1 For order two, the rate coefficient has units of L mol 1 s 1 (or M 1 s 1 ) And for order three, the rate coefficient has units of L 2 mol 2 s 1 (or M 2 s 1 ) 33. Define collision theory. Write the expression relating the rate of the reaction with temperature. The collision theory states that when suitable particles of the reactant hit each other, only a certain percentage of the collisions cause any noticeable or significant chemical change; these successful changes are called successful collisions. The successful collisions have enough energy, also known as activation energy, The rate constant for a bimolecular gas phase reaction, as predicted by collision theory is: where: Z is the collision frequency. ρ is the steric factor. Ea is the activation energy of the reaction. T is the temperature. R is the gas constant. PART-B QUESTIONS 1. (i) Derive the Michaleis-Menten equation for the enzyme substrate reaction. E + A X E + P. State also the assumptions made. (Dec13, 15 &May 13, 16) Enzymes are nature s catalysts. The vast majority of chemical reactions that keep living things alive are much too slow to sustain life. An example is oxidation of a sugan say glucose to give water, carbon dioxide and energy. You can leave glucose open to the air for years without any appreciable oxidation, yet this is one of the reactions that provides the energy to walk and run in daily life. There are diseases caused by the failure of the body to produce a specific enzyme. The Michaelis-Menten mechanism for the catalysis of biological chemical reactions is one of the most important chemical reaction mechanisms in biochemistry. The michaelis menten mechanism for the enzyme kinetics is; k 1 E + S ES K2 E + products k 1 E is the enzyme, S is the substrate and ES is an enzyme-substrate complex. We analyze this mechanism as ususal. First, we define the reaction rate as the rate of formation of product and write the kinetic equation implid by this mechanism, d[product] = k dt 2 [ES] The enzyme-substrate complex, ES is a transient species so we set up an equation for its rate of change and apply the steady state approximation, d[es] = k dt 1 [E][S] K 1 [ES] K 2 [ES] 0 Solve for [ES], [ES] = k 1 [E][S] K 1 + K 2, and substitute it in to the equation for the rate, VTHT 7

8 Rate = d[product] dt Introducing the Michaelis-Menten Constant, K M 1 K M = So that the rate becomes, = k 2 k 1 [E][S] K 1 + K 2 k 1 K 1 + K 2 Rate = k 2 [E][S] K M [E] is the concentration of free enzyme and this is usually not known. [E 0]is the total enzyme concentration, but [E] 0 = [E] + [ES] = [E] + [E][S] K M = [E] (1 + [S] ) K M From which we obtain, [E] 0 [E] = (1 + [S] ) K M The rate becomes, then Rate = k 2 [E] 0 [S] K M (1 + [S] ) K M [E] 0 [S] = k 2 (1 + [S] ) K M Define the reaction velocity as ν = Rate. So, [E] 0 [S] ν = k 2 (K M + [S]) Note that the reaction velocity, υ, is zero whe [S] is zero and that the reaction velocity increases as we increase [S]. The reaction velocityreaches a maximum when [S] becomes very large. Define the maximum velocity, υ max,as Then, ν max = lim [S] 0 k 2 [E] 0 [S] (K M + [S]) = k 2[E] 0 ν = ν max[s] K M + [S] Note, the kinetics of the reaction are characterized by two parameters, υ max and K M 1 ν = K M ν max [S] + 1 ν max In this experiment one measures ν as a function of [S]. if we plot 1/ νagainst 1/[S] we should get straight line with slope, K M/ν max and intercept 1/ν max. slope K M = slope ν max = intercept (ii) Explain the effect of temperature on the reaction rate according to collusion theory. (Dec15, May 16) Let's consider the following gas-phase elementary reaction: A + B products The reaction rate is straightforwardly: VTHT 8

9 Recall previous discussions of the total collisional frequency for heterogeneousreactions: where the the following: are number of molecules /particles per unitvolume. We can see Here we see that the concepts of collisions from simple kinetic theory can befundamentally related to ideas of reactions, particularly when we considerthat elementary reactions (only for which we can write rate expressionsbased on molecularity and order mapping) can be thought of proceeding due to collisions (or interactions of some sort) of monomers (unimolecular),dimers(bimolecular), trimers (trimolecular), etc. If we are to naively say that reactions occur due only to collisions of particles(keep in mind the nature of the system { gas-phase,elementary reaction),then we can at the zero'th order equate the maximum reaction rate to thetotal collisional frequency for heterogeneous pairs: Simple Collision Theory: Caveats Simple collision theory (SCT), we see from above, remarkably predicts anexpression for the microscopic rate constant that relates to the dimensions ofthe reactive species, their mass, and temperature. The form we determinedabove assumes two things: All collisions are of su_cient energy that chemical transformation canoccur Steric/orientational nature of collision is always correct/accommodating. VTHT 9

10 Thus, we need to consider the effects of collision energy and collisionsterics and/or orientation in our discussion of simple collision theoryand its application to de_ningthe reate constant, k. For energetic considerations, we can empirically add a factor to accountfor the probability of a collision having a suffcient energy,vis-a-vis, E min, for collision. When we multiply the total collisionalfrequency by this probability, we can describe the fraction of collisionsthat will energetically be able to progress from reactants to products. The energy probability is take to be Boltzmann-like: For steric/orientational nature of collision, we introduce a steric factor(empirically), p p < 1 generally Thus, we can write a more general expression for the collision theory based reaction rate as: Thus we arrive at a corrected Simple collision theory expression for the rateconstant: Note the temperature dependence of the rate constant with SCT: In general, we can write this expression for the rate constant as: 2. The irreversible reaction A + B AB has been studied kinetically and the rate of formation of 2 product has been found to be well correlated by the following equation; r AB = k C B (independent of C A). What reaction mechanism is suggested by this rate expression, if the chemistry of the reaction suggests that the intermediate consists of an association of reactant molecules and that chain reaction does not occur? (May-2008) Refer, Chemial Reaction Engineering by Octave Levenspiel, 3 rd Edition Page NO The decomposition of reactant A at 400 o C for pressures between 1 and 10 atm follows a firstorder rate law. Show that the mechanism, A + A A * + A & A * R + S is consistent with observed kinetics. (Dec-2003 & May-2006) VTHT 10

11 4. Explain the effect of temperature on reaction rate according to the transition state theory and compare with other theories. (May-2016, May 2013) For elementary reactions, the rate expression can be written as a product of a temperature-dependent term and a composition dependent term, For such reactions the temperature-dependent term, the reaction rate constant, has been found in practically all cases to be well represented by Arrhenius law: k = k 0e -E/RT Where k 0 is called the frequency or pre-exponential factor and Eis called the activation energy of the reaction. At the same concentration, but at two different temperatures, Arrhenius law indicates that Provided that E stays constant. Comparison of theories with Arrhenius law The expression Summarizes the predictions of the simpler versions of the collision and transition state theories for the temperature dependency of the rate constant. For more complicated versions m can be as great as 3 or 4. Now, because the exponential term is much more temperature-sensitive than the preexponential term, the variation of the latter with temperature is effectively masked VTHT 11

12 5. (i) The pyrolysis of ethane proceeds with an activation energy of about 300 kj/mol. How much faster is the decomposition at 650 C than at 500"C? (Dec 2015) (ii) Milk is pasteurized if it is heated to 63 o C for 30 minutes, but if it is heated to 74 o C it only needs 15 seconds for the same result. Find the activation energy for this sterilization (May-2006) Assuming Arrhenius temperature dependency for the process Now the rate is inversely proportional to the reaction time or rate 1/time or from which the activation energy E = J/mol 6. Explain the Integral and Differential method of analysis for finding the rate of reaction. (May05) One of the purposes for which batch reactors are used is rate law determination. Concentration (or any other convenient variable) measured as a function of time is the data typically available Several methods are available for this analysis - differential, integral, initial rate, half life, etc. Differential Method VTHT 12

13 data is available as C A vs. t (where A is a reactant) for constant volume batch reactor with nth order reaction we can write or, thus if we can plot From the data, we will get a straight line whose slope gives the order of the reaction and whose intercept gives the logarithm of the rate constant. But how to get dc A given data of CAvs. time? dt several methods exist for this as well - numerical differentiation, graphical method, and polynomial fit method Numerical Differentiation in this method, the derivative is evaluated using finite difference formulas, where i refers to the number of the data point. Such formulas can be forward or backward difference. A three-point differentiation formula in general will give more accurate results than the above: the data should have been collected in equal time intervals Graphical Method * in this method, a smooth curve is drawn through the experimental data points on a C Avs. t graph. * at each time instant of interest, tangents are drawn to this curve, the slope of the tangent line is the derivative value at that time instant * this method is attractive since we have a lot of control over the quality of results, and no assumptions regarding uniformity of sampling time intervals, etc. are required. * but it can be tedious, specially for large data sets or many experiments. Polynomial Fit Method * a polynomial of suitable order has to be fitted to the data * the derivative can be then evaluated by differentiating the polynomial expression * extreme care is necessary to make sure the fit is sensible - in general the best lower order polynomial that fits the data reasonably should be chosen rather than a very high order polynomial that goes through all the data points * a plot of the data and the fitted polynomial curve can be an important visual tool to ascertain that we doing the sensible thing Differential Method, non-constant volume batch reactor * similar analysis is possible for non-constant volume batch reactor * lets say that V (total volume) is the measured variable * balance equation is written as VTHT 13

14 Thus, Or, and thus a straight line plot can be obtained to get the order or reaction from V vs. t data Integral Method * an order of reaction has to be assumed * then the batch reactor equation is integrated with the rate law of assumed order * the quantities are bunched together in such a manner as to get a linear equation * plot the data for this line * the assumed order is correct if the data actually fall on this line, if not, another trial is required * the slope and intercept of this straight line should give the rate constant value 7. Aqueous A at a concentration C Ao = 1mol/lit is introduced into a batch reactor where it reacts away to form product R according to stoichiometry A R. The concentration of A in the reactor is monitored at various rates as shown below; t (min) C A (mol/m 3 ) For C Ao = 500mol/m 3 find the conversion of reactant after 5 hours in the batch reactor. Find the rate for the reaction also. (Dec-2003) Solution: For 1 st order reactiona R, the rate equation is We Know, C A0 = 1 mol/lit = 1000 mol/m 3 ln ( C A C A0 ) = ln( 1 x A ) = kt t (min) C A (mol/m 3 ) C A/C A0 -ln (C A/C A0) VTHT 14

15 Plot -ln (C A/C A0)Vstime(t) Slope gives; k- rate constant, rate constant is a constant value for same order reactions. Therefore, equate the value for initial concentration C A0 = 500 mol/m 3. ln ( C A C A0 ) = kt ln ( C A ) = k(slope value) C A = calculate the value. Now, we know, C A = C A0 (1 x A ), using this equation we can calculate x A 8. The following data are obtained at 0 o C in a constant-volume batch reactor using pure gaseous A; t, min p A, mmhg The stoichiometry of the decomposition is A 2.5 R. Find a rate equation. (May-2006) VTHT 15

16 9. The first order reversible liquid reaction A P, C Ao = 0.5 mol/lit &C Po = 0, takes place in a batch reactor. After 8 minutes, conversion of A is 33.3% while equilibrium conversion is 66.7%. Find the rate equation for this reaction. (May-2009) VTHT 16

17 10. When a concentrated urea solution is stored it slowly condenses to biuret by the following elementary reaction: 2 NH 2-CO-NH 2 NH 2-CO-NH-CO-NH 2 + NH 3 To study the rate of condensation a sample of urea (C = 20 milliliter) is stored at 100 C and after 7 hr 40 min we find that 1 mol% has turned into biuret. Find the rate equation for this condensation reaction. VTHT 17

18 11. Substrate A is converted to product by the action of enzyme, a high molecular weight (mw > 10000) protein like substance. An enzyme highly specific, catalyzing one particular reaction or one group of reactions. Thus A enzyme R (May 2012) Many of these reactions exhibit the following behavior: i. A rate proportional to the concentration of enzyme introduced in to the mixture [E 0]. ii. iii. At low reactant concentration the rate is proportional to the reactant concentration, [A]. At high reactant concentration the rate levels off and becomes independent of reactant concentration. (Propose a mechanism to account for this behavior) Refer 12. Explain : (May 2012) i. Arrhenius theory In general, experiments do not suggest a T 1/2 temperature dependence of therate constant. Moreover, experiments demonstrate for most reactions thatthe temperature dependence of ln(k) is linear with 1/T. Thus, Arrhenius proposed the following relation between temperature and the rate constant: Thus, The energy is the activation energy (as discussed above) and the A value isa temperature-independent frequency factor, or pre-exponential factor. Plotting ln(k) versus T-1 will yield a straight line with slopeequal to E a R and y intercept of ln(a). R The pre-exponential factor in this case if independent of temperature, contrastedwith the SCT result from above. Though many reactions (across thespectrum of reaction orders, mechanisms, etc.) follow Arrhenius behavior,there are exceptions (as always). ii. Order and molecularity of a reaction Moleculariy Order of Reaction It is the total number of reacting species (molecules, atoms or ions) which bring the chemical change. It is the sum of powers of molar concentration of the reacting species in the rate equation of the reaction. It is always a whole number. It may be a whole number, zero, fractional, It is a theoretical concept. It is experimentally determined. It is meaningful only for simple reactions or individual steps of a complex reaction. It is meaningless for overall complex reaction. It is meant for the reaction and not for its individual steps VTHT 18

19 iii. Fractional conversion and extent of reaction Extent of Reaction (ε) The extent of the reaction is an extensive quantity describing the progress of a chemical reaction. Depends on the degree of completion of the reaction. Where, N i = molar amount remaining of species I N i0 =initial amount in the feed v i=stoichiometric coefficient (+ for product, - for reactants) ε = extent of reaction iv. Single reactions and multiple reactions Find the overall order of the irreversible reaction (Dec 2012) 2H 2 + 2NO N 2 + 2H 2O From the following constant-volume data using equimolar amounts of hydrogen and nitric oxide: Total pressure, mm Hg Half-life, sec Solution: t 1/2 = 0.5(1 n) 1 k(1 n) (1 n) t 1/2 C A0 t 1/2 ( P (1 n) A0 RT ) (1 n) C A0 t 1/2 = ( 1 (1 n) RT ) (1 n) P A0 Taking Log on both sides, Log t 1/2 = log k + (1-n) log P A0 For equimolal amount of A&B P A0 = P B0 We know, P 0 = P A0 + P B0 P A0 = P 0/2. Convert the give t 1/2 values and P A0 values in to its log form. Plot graph for given linear equation and fine slope value (1-n). From which we can fine overall order(n) of the reaction. 14. For the irreversible reaction in series, (May 2013) A K 1 R K 2 S. Derive an expression for the maximum concentration of intermediate product R. VTHT 19

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21 VTHT 21

22 15. (i) At 500K the rate of bimolecular reaction is ten times at 400 K. Find the activation energy for this reaction from Arrhenius law and collision theory. If the rate of reaction at 600 K thepercentage difference by this two methods. (May & Dec 2015) Arrheniu s law ln r 2 r 1 = E R ( 1 T 1 1 T 2 ) r 1 = rate at 400K r 2 = rate at 500K Given r 2 = 10r 1 Sub in equation and find r 1 and then K. Rate constant (K) is constant for same order reaction. Therefore, we can sub in rate equation to find rate at 600K. Similarly do for Collision Theory for the given rate equation. (ii)rahul likes to play the gambling tables just to get relaxed. He never expects to win and he does not, so he selects games in which he losses are given small fraction of the money bet. He plays steadily without a break, and the sizes of his bets are proportional to the money he has, if at gambling table -1 it takes four hours to lose half of his money and at table-2 it takes two hours to lose half of his money, how long can he play at both the tables simultaneously if he starts with Rs and quit when he has 10? (Dec 2015) VTHT 22

23 (ii) Write the difference between molecularity and order of the reaction. (May 2015) S.NO MOLECULARITY OF REACTION ORDER OF REACTION 1 It is defined as the number of molecules atoms or ions participating in rate determining step of the reaction. It is defined as the sum of the exponents of the concentration terms in rate equation. 2 It is theoretical quantity to satisfy the It is entirely an experimental experimental findings. 3 It must be a whole number and never be zero or a fraction. quantity. It may be a whole number, zero or a fraction. 16. (i) Explain in detail about industrial scale bioreactors with suitable diagrams. (May 2015) Based on flow pattern: Plug flow and Tubular flow reactors. Based on mode of operation: Batch, fed batch, CSTR. Eg.Fluidised bed reactors (ii) 2N 2O 2N 2+O 2 according to second order rate reaction. The reaction rate is 977 cm3/(mol.s) at 895C. Calculate the fraction decomposed at 1s 10s and 10 minutes in a constantvolume batch reactor. The initial pressure is 1 atm. Write and take photo UNIT-II IDEAL REACTORS PART-A QUESTIONS & ANSWERS 1. What are the different factors to be considered for reactor design? The different factors required for reactor design are (i) Size of reactor (ii) Type of reactor (iii) Time or duration of reaction (iv) Temperature & Composition of reacting material in the reactor (v) Heat removal or added and (vi) Flow pattern of fluid in the reactor. 2. What are ideal reactors? Ideal reactors (BR, PFR, and MFR) are relatively easy to treat. In addition, one or other usually represents the best way of contacting the reactants no matter what the operation. For these reason, VTHT 23

24 we often try to design real reactors so that their flows approach these ideals. 3. What is a Batch reactor? (Dec 2012) A batch reactor (BR) is one in which reactants are initially charged into a container, are well mixed, and are left to react for a certain period. The resultant mixture is then discharged. This is an unsteady state operation where composition changes with time; however at any instant the composition throughout the reactor is uniform. 4. What are the advantages and disadvantages of a batch reactor? The advantages of a batch reactor are (i) small instrumentation cost and (ii) flexibility of operation.a batch reactor has the disadvantages of (i) high labour (ii) poor quality control of the product and (iii) considerable shutdown time has taken to empty, clean out and refill. 5. What is a Mixed flow reactor? Mixed flow reactor (MFR) is also called as back mix reactor or continuous stirred rank reactor (CSTR) or constant flow stirred tank reactor (CFSTR). In this reactor, the contents are well stirred and uniform throughout. The exit stream from the reactor has the same composition as the fluid within the reactor. 6. What is a Plug flow reactor? (May 2011) Plug flow reactor (PFR) is also referred as slug flow, piston flow, and idealtubular and unmixed flow reactor. It specifically refers to the pattern of flow as plug flow. It is characterized by the fact that the flow of fluid through the reactor is orderly no element of fluid overtaking or mixing with any other element ahead or behind. Actually, there may be lateral mixing of fluid in a PFR; however, there must be no mixing or diffusion along the flow path. The necessary and sufficient condition for plug flow is the residence time in the reactor to be the same for all elements of fluid. 7. Differentiate between MFR and PFR. MFR: i) there is no concentration gradient within the reactor, since there is uniform mixing. ii) Rate of reaction varies with concentration alone. PFR: i) There is concentration gradient within the reactor in the axial direction, since there is no mixing in this direction. ii) Rate of reaction varies with position. 8. Define space time & space velocity. (May 2013, 14, 15& 16, Dec 15) The time required to process one reactor volume of feed measured at specified conditions is called space time. Space velocity is defined as the number of reactor volumes of feed at specified conditions which can be treated in unit time. 9. Explain conservation of mass in reactors. Rate of accumulation of the component within the system = Rate of flow of a intothe system Rate of flow of A out of the system Rate of consumption of component a in the System. 10. Write the classification of chemical reactors based on the method of operation and the number of phases in the reaction mixture. Method of operation: Unsteady state reactors batch and Semi-batch Steady state reactor Tubular reactor, Back mix Phases: Homogeneous reactor Batch, PFR, MFR reactors Heterogeneous reactor Biochemical Reactor 11. Distinguish between Holding time and Space time for flow reactors. Holding time: It is the mean residence time of flowing material in the reactor. It is given by the expression t = C Ao dx A / [(-r A) (1 + A X A)] Space time: It is the time needed to treat one reactor volume of feed at specified conditions. It is given by the expression, = V/v o = (C Ao V) / F Ao For constant density systems (all liquids and constant density gases) t = = V/v. Where V is the volume of the reactor and v is the volumetric flow rate of reacting fluid. 12. Consider a gas phase reaction 2A R+2S with unknown kinetics. If a space velocity of 1min -1 is needed for 90% conversion of A in a PFR find the corresponding space time and mean residence time or holding tome of the fluid in the reactor. Given, X A=0.9, space velocity=1 min -1. (i) Space time=1/space velocity=1 min. (ii) = V/v f = V/v o (1 + AX A ); where A = (3-2)/2 = 0.5 and V/v 0 = 1 Therefore, = V/v f = V/v o (1 + A X A) = 1/1.45= min. VTHT 24

25 13. A 2 nd order reaction is to be carried out in 3 CSTR s of Volume 100 lit, 150 lit and 200 lit. Explain how they are connected. For 2 nd order (n > 1) reaction, to be carried out in CSTR s of different sizes,the reactors should be ordered so as to keep the concentration of reactant as high as Possible. This can be performed by arranging them in the ascending order with respect to volume or size. Hence, the best arrangement should be 100 liter 150 liter 200 liter 14. Differentiate between PFR and Batch reactor. PFR: (i) It is a steady state flow reactor (ii) As space time increases concentration of reactant decreases (iii) Better quality control (iv) For high rate of reaction PFR is employed. Batch reactor: (i) It is unsteady state reactor (ii) As reaction time increases concentration of reactants decreases (iii) No better quality control (iv) For very slow reactions or low rate of reaction batch reactors are employed. 15. What are steady and unsteady state reactors? Explain. Steady state reactor: Reactors those in which the properties of the system do not change with time is said to be a steady state reactor. Example: Continuous stirred Tank reactor, plug flow reactor.total mass inflow = Total mass outflow Unsteady state reactor: Reactors are those in which the properties of the system changes with time and rate of reaction decreases with time expect for zero order reaction are said to be unsteady state reactor. Example: Batch reactor, Semi-batch reactor. There is accumulation in these reactors. Accumulation = input - output + generation - consumption. 16. What are semi batch reactors? Give the different types. (Dec 2012) It is an unsteady state reactor. Reactors which are partially batch and partially continuous are referred to as semi-batch reactor. The semi batch reactors offers good control of reaction speed, because the reaction proceeds as reactants are added. Types: (i) volume changes but composition is unchanged (ii) composition changes but volume is constant. 17. Which achieves higher conversion among the flow reactors for identical conditions? Why? For identical conditions i.e. for some reactor volume conversion achieved in PFR is higher than in MFR. Since in a PFR, all the properties vary gradually along the length of the reactor. Hence concentration is maintained at high value throughout and the rate of reaction is maintained at high value. Therefore Conversion achieved in PFR for same volume is greater or higher than in MFR. 18. Why does rate of reaction vary in a PFR? How does it vary in a MFR? Rate of reaction varies, for isothermal reactions, in PFR as there is no mixing in the axial direction since rate of reaction is directly proportional to concentration. As concentration of reactant varies with distance rate of reaction also varies. In PFR, rate of reaction is independent of time and dependent on position or distance.in MFR, rate of reaction is independent of position &dependents on concentration of reactants. 19. For two CSTR s operating in series, state the principle involved to determine the minimum volume of reactors. Given, feed concentration is C AO and final concentration is C A2. The reaction is first order. For a system of two CSTR s connected in series, in which first order reaction is taking place and for the given conversion, the minimum volume of reactors will be obtained when both the reactors are operated with equal volume. This was obtained by using the minimum concentration of A as C A, MIN = SQRT (C AO C A2) inthe performance equation. 20. How does intermediate conversion affect the volume of the multiple reactor system for single reactions? Intermediate conversion affects the volume of the multiple reactor system for single reactions in case of MFR only.in case of PFR intermediate conversion does not determine the total reactor volume; in the case of PFR s whatever be the intermediate conversion the total reactor volume required to achieve a given conversion is identical.in case of MFR, there is a particular intermediate conversion. At this conversion the total volume of the reactor required is minimum. Thisconversion is called as the best intermediate conversion. If the intermediate conversion is changed the size ratio and volume of the units will change. 21. A large CSTR, small CSTR and PFR of fixed volume are available. In general, how would you arrange them for getting maximum conversion for reactions of order >1 and <1. Why? VTHT 25

26 For n>1 arrangement is PFR followed by small CSTR followed by large CSTR to maintain the reactant concentration as high as possible. For n<1 arrangement is large CSTR followed by small CSTR followed by PFR. For n=1 arrangement for first order reaction sequencing does not affect conversion. It can be either PFR followed by MFR or MFR followed by PFR. 22. If 1/(-r A) versus X A graph decreases to a minimum from X A = 0 to X A = 0.4 and then increases, suggest a multiple reactor system with minimum volume for a desired conversion of X A = 0.6. For the given situation, the best reactor setup should be PFR followed by CSTR. That is, PFR should be operated up to the point of minimum (up to X A = 0.4) followed by a CSTR to fulfill the desired conversion (X A = 0.6). Because minimum the area under the curve of 1/(-r A) versus X A will lead to the minimum volume for the desired conversion. This was obtained only by the above said reactor arrangement. 23. What is a Recycle reactor? In some reaction system, it is advantageous to divide the product stream and a part returned to reactor as recycle to increase the conversion rate. These reactors are called recycle reactors. The recycling provides a means for obtaining various degree of backmixing. 24. Define Recycle ratio and give its significance Recycle ratio R can be defined as the ratio of the volume fluid returned to the reactor entrance to the volume of fluid leaving the system or reactor. Significance: Recycle ratio can be made to vary from zero to infinity. Reflection suggests that as the recycle ratio is raised, the behavior shifts from plug flow (R = 0) to mixed flow (R = ). 25. What do you mean by optimum recycle operation? When material is to be processed to some fixed final conversion in a recycle reactor, there must be a particular recycle ratio R that minimizes the reactor volume or space time. That recycle ratio is said to be optimum and the operation is said to be optimum recycle operation. 26. Suggest the most suitable reactor setup for all autocatalytic reactions. The most suitable reactor setup for autocatalytic reactions is MFR operating at the point of maximum rate (low conversion) followed by a PFR (high conversion); that is, MFRoperating to maximum rate followed by PFR. Because this will lead to a system with minimum volume for a desired conversion. 27. Define instantaneous and overall fractional yield. Instantaneous fractional yield ( ) is the ratio of moles of desired product formed at any instant to moles of reactant (A) reacted at any instant. is a function of C A. As C A varies throughout the reactor, will also vary with position in the reactor. Overall fraction yield ( ) is the mean of the instantaneous fractional yields at all points within the reactor.both the yields depend on the type of flow within the reactor. 28. Explain the term Selectivity and Yield. Selectivity is defined as the ratio of moles of desired product to moles of undesired product.yield is defined as the ratio of moles of product formed to moles of reactant either fed or consumed. 29. What are the factors affected by the pattern of flow within the vessel for multiple reactions? The factors affected by the pattern of flow within the vessel for multiple reactions are (i) The Volume of the vessel, (ii) The product distribution, (iii) Selectivity and yield of product. 30. How will you control the product distribution for reactions in parallel using k 2/k 1? The product distribution for reactions in parallel can be controlled by varying the ratio k 2/k 1 (ratio of the rate constants of the formation of undesired product to the desired product). This can be done in two ways; By changing the temperature level of operation. (If the activation energy of the two reactions are different, k 2/k 1 can be made to vary.) By using a catalyst. (One of the most important features of catalyst is its selectivity in depressing or accelerating specific reactions. This may be a much more effective way of controlling product distribution than any other way.) 31. How does the concentration level of reactants affect the product distribution in parallel reactions? (May 2012) For reactions in parallel, the concentration level of reactants is the key to proper control of product distribution. That is, i) High reactant concentration favors the reaction of higher order. ii) Low reactant concentration favors the reaction of lower order. iii) The concentration level has no effect on the product distribution for reactions of the same order. VTHT 26

27 32. Write the general representation of series-parallel reactions with an example. T T is Parallel with respect to A and series with respect to A, R, and S. (ii) A + B R and R + B S Parallel with respect to B and Series with respect to A, R, and S. 33. Explain the best operating conditions for parallel reactions. For a desired conversion, the best operating condition for parallel reactions is that the reaction should be performed in the MFR first, up to the maximum yield withrespect to theconcentration of reactant in the (S/A) versus C A, and the followed by a PFR up to the desired conversion. Here, S is the desired product. 34. Describe briefly on multiple reactions. There are three basic types of multiple reactions: series, parallel, and independent. In parallelreactions (also called competing reactions) the reactant is consumed by two different reactions to form different products: In series reactions, also called consecutive reactions, the reactant forms an intermediate product, which reacts further to form another product: Multiple reactions involve a combination of both series and parallel reactions, Independent reactions are of the type and occur in feed stocks containing many reactants. The cracking of crude oil to form gasoline is an example of an independent reaction. 35. Write the assumptions made in the design equation of (May 2014& Dec 15) (i) Batch reactor (ii) Plug flow reactor Batch Reactor: Closed system: no streams carrying mass enter of leave the system. No ideal flow or out flow, F A0 = F A = 0 Well mixed, no spatial variation in system properties Constant volume, V= V 0or Constant pressure Plug Flow Reactor: Steady state No radial variation in properties of the system. 36. Write the simpson 1/3 rule and explain the variables. (May 2016) Simpson's rule is a Newton-Cotes formula for approximating the integral of a function using quadratic polynomials (i.e., parabolic arcs instead of the straight line segments used in the trapezoidal rule). Simpson's rule can be derived by integrating a third-order Lagrange interpolating polynomial fit to the function at three equally spaced points. In particular, let the function be tabulated at points,, and equally spaced by distance, and denote. Then Simpson's rule states that PART-B QUESTIONS 1. Derive the performance equation formixed flow reactor.(dec-2004 & Dec-2005) We know the composition is uniform throughout the reactor. Select reactant A Input = output + disappearance by reaction + accumulation VTHT 27

28 Introducing these three terms we obtain, On rearrangement the equation becomes, 2. A homogeneous gas reaction A 3R has a reported rate at 215 o 1/2 C as -r A = k C A mol/lit-sec. Where k =10-2. Find the space time needed for 80% conversion of 50% A and 50% inert feed to PFR operating at 215 o C and 5 atm. (May-2008) Solution: For 50% inerts, ε 4 2 A = 2 =1 Substitute in Plug flow performance equation, The integral is evaluated by graphical method by assuming the values of A in an equal interval. X A = 0 1 Plot graph by taking X A in x-axis and ( 1+X A 1 X A ) 1/2 in y-axis. Find out the area under the square to determine the space time. 3. The kinetics of the aqueous phase decomposition of A is investigated in two mixed reactors in series, the second having twice the volume of the first reactor. At steady state with a feed concentration of 1 mol(a)/liter and mean residence time of 96 seconds in the first reactor, the concentration in the first reactor is 0.5 mol(a)/liter and in the second is 0.25 mol(a)/liter. Find the kinetic equation for the decomposition. (Dec-2005) VTHT 28

29 4. A liquid reactant stream (1 mol/lit) passes through two MFR s in series. The concentration in the exit stream of the first reactor is 0.5mol/lit. Find the concentration in the exit stream of the second reactor. The reaction is second order with respect to A and V 2/V 1 =2 (May-2008) 5. Originally we had planned to lower the activity of a gas stream containing radioactive Xe-138 (halflife = 14 min) by having it pass through two holdup tanks in series, both well mixed and of such size that the mean residence time of gas is 2 weeks in each tank. It has been suggested that we replace the two tanks with a long tube (assume plug flow). What must be the size of this tube compared to the two original stirred tanks, and what should be the mean residence time of gas in this tube for the same extent of radioactive decay? (Dec-2007) VTHT 29

30 6. Consider the parallel decomposition of A of different orders, S is desired product andc Ao = 4mol/lit, R r R = 1 A S r S = 2 C A T r T = C A 2 Find the maximum expected C S for isothermal operations (i) in a MFR & (ii) in a PFR 7. A concentrated aqueous A-solution of the previous examples (C A0 = 4 mol/liter,f A0= 1000 mol/min) is to be 80% converted in a mixed flow reactor. (a) What size of reactor is needed? (b) What is the heat duty if feed enters at 25 C and product is to be withdrawn at this temperature? Note that C pa = 1000 cal kg. K. 1 kg 1 liter. 1 liter 4 mol A = 250 cal mol A. K VTHT 30

31 VTHT 31

32 8. We wish to treat 10 liters/min of liquid feed containing 1 mol A/liter to 99% conversion. The stoichiometry and kinetics of the reaction are given by C A mol A R, r A = C A liter. min Suggest a good arrangement for doing this using two mixed flow reactors, and find the size of the two units needed. Sketch the final design chosen. 9. Derive the space time and space velocity equations for the steady state MFR and PFR and also give the graphical representations of the design equations. (Nov 2010& Dec 15) Refer Octave Levenspiel Page No; 94-96(MFR) and (PFR). 10. At present we have 90% conversion of a liquid feed (n = 1, C A0, = 10 mol/liter) to our plug flow reactor with recycle of product (R = 2). If we shut off the recycle stream, by how much will this lower the processing rate of our feed to the same 90% conversion? (Dec 2011) VTHT 32

33 11. A batch reactor is designed to convert A into R. this is aliquid reaction. The stoichiometry is given by A R and the rate of reaction is given in the following table. How long must the batch for the concentration to drop from 1.3 mol per liter to 0.3 mol per liter. (May 2013) C A (mol/lit) r A(mol/lit.min) (i) Discuss different types of reactors used for carrying out reactions. (Dec 2012) (ii) Derive the equation to find out optimum T and C R/C Ao in mixed flow reactor for the reaction. A R S Refer Octave levenspiel page no: A gaseous feed of pure A with C A0 = 1 mol/l enters a mixed flow reactor of 2-liter volume and reacts to give R. The reaction kinetics and stoichiometry are given by 2A -> R, -r A=0.05C A2mol/(l.s). Find the feed rate (l/min) that will give an outlet concentration C A=0.5 mol/l. (May 2015) 14. Derive the design equation for ideal batch reactor and CSTR. (May 2016) Refer Class Notes. 15. A homogeneous liquid phase reaction A R with reaction rate r A = kc A 2 takes place with 50% conversion in a mixed reactor. (May 2016) (i) What will be the conversion if this reactor is replaced by one, six times as large, other factors remaining unchanged? (ii) What will be the conversion if the original reactor is replaced by a PFR of equal size, other parameters unchanged? 16. In a hydrolysis reaction Sucrose sucrase Product with reaction rate, r A = KC AC Eo C A +M, where M is the Michaeli s menten constant. Show by calculation whether the following data can be reasonably fit the kinetic equation. Evaluate the constants k and M. (Dec 16) Time (t) C Ammol/l VTHT 33

34 UNIT-III IDEAL FLOW AND NON IDEAL FLOW PART-A QUESTIONS & ANSWERS - CO What are the differences between ideal and non-ideal reactors? Ideal reactor i) Mean residence time tm is the same for both PFR &MFR. Because in an ideal CSTR since there is perfect mixing most of the molecules leave the reactor around the mean residence time. ii) There is no bypassing or short-circuiting and no dead zone formation. Yield is more, as conversion is more. Non-ideal reactor i) In non-ideal tubular reactor distribution of residence time is there. Even in non-ideal CSTR, there is residence time distribution.in case of non-ideal tubular reactor each and every element or molecule will not have same residence time. ii) There might be bypassing or short-circuiting & Yield is low. 2. Explain the term Channeling. (May 2013) This takes place in a packed bed reactor. When a reactor is packed with catalytic material, the reacting fluid does not flow uniformly. Some sections of the packing offer little resistance to flow and VTHT 34

35 so major portion of fluid channels through this path. 3. Explain the term short-circuiting. (May 2013) In many Cases, the inlet and outlet pipes are closed together. Therefore some molecules that enter the reactor leave immediately through the exit. This phenomenon is called as Short-circuiting. 4. Explain the relation between I and E of a perfectly mixed CSTR. I of a perfectly mixed CSTR am equal E because the composition of the effluent at the exit is identical to the composition of material anywhere within the CSTR as it s a perfectly mixed CSTR. 5. Name the zero parameter models used to characterize non-ideal flow in vessels. (May 2012) i) Maximum mixed ness model Molecules of different age group are completely mixed at the molecular level as soon as they enter the reactor. This is called as complete micro mixing or maximum mixed ness model. ii) Complete segregation model All molecules of same age group remain together as they travel through the reactor and are not mixed till the exit point. This is called as completes segregation model. 6. Define the term RTD. How does it help in characterizing non-ideal reactors? (May2011& 2014) Fraction which gives the percentage of molecules leaving the reactor that spends a time between t and t+ t inside the reactor. It s the function that describes how much different fluid elements have spent inside the reactor. From RTD data we can predict the reactor volume. 7. Give the name of the experimental technique used to study non-ideal flow in vessels. STIMULUS RESPONSE TECHNIQUE - The stimulus is a tracer input in to the fluid entering the vessel. The response is a time record of tracer leaving the vessel. 8. What are the signals used to study non-ideal flow? Draw the common output curves for the same. i) random input. ii)periodic input iii) Step input iv)pulse input. 9. Define F curve. A time record of tracer in the exit stream from the vessel measured by C/C o, by giving step input, is called as F-curve. 10. When Non-ideal flow occurs in reactors? or what are the reasons for non-ideality in real reactors? (May 2012) The non-ideal flow occurs due to (i) Channeling (ii) Recycling (iii) by creation of stagnant regions (iv) by passing or short circuiting. (v) formation of vortices and turbulence at inlet and outlet, in the reactors. 11. Define closed vessel. The closed vessel is defined as one in which fluid enters and leaves solely by plug flow, thus with the flat velocity profile. 12. What is internal Age distribution? It is function which gives the fraction of material inside the reactor that has been inside for a period of time between and +. It is denoted by the letter I. 13. Define open vessel. The open vessel is defined as one in which the flow of fluid is undistributed as it passes the entrance and exit boundaries. 14. Explain about a Delta function. With no trace initially present impose an idealized instantaneous pulse of tracer on the stream entering the vessel. Such an input is called a delta function. 15. What is meant by Linear process? A process is Linear if any change in magnitude of the stimulus results in a corresponding proportional change in the magnitude of the response. 16. What are Dispersed model? The models which are on analogy between mixing and actual flow and a differential process to characterize non-ideal flow within vessels are called dispersed model. 17. What are the assumptions of Plug Flow? How does the dispersion model account for nonideality in flow? i) Velocity profile is flat - No diffusion (or) mixing along axial direction. ii) Dispersion model is used to describe non ideal tubular reaction. In this model, there is an axial dispersion of the material which is governed by an analogy to Fick s law of diffusion; super imposed on the flow.so, in addition to bulk flow energy component in the mixture is transported through any cross section of the reactor by diffusion. 18. How the distribution of different lengths of time for the stream of fluid leaving the vessel VTHT 35

36 called? The distribution of different lengths of time for the stream of fluid leaving the vessel is called (i) The Exit age distribution E (ii) The residence time distribution RTD of fluid. 19. Define Turnover time. The time between successive peaks characterizes fluid regulation is called turnover time. 20. Give the relationship between E and F curves. The relationship between E and F curves for the fraction of the exit stream that has resided in the reactor for a period of time shorter than a given value t is given by t E(t) dt = [Fraction of effluent which has been in the reactor for less than time t ] 0 = F(t) (or) df/dt = E(t) 21. State the one parameter in the dispersion model and state its limitations. The one parameter in the dispersion model is Vessel dispersion number [D/(U L)], which measures the extent of axial dispersion. When D/(U L) 0, real reactor will behanve as ideal PFR and D/(U L), real reactor will behanve as ideal MFR.Where D is the dispersion or diffusion coefficent, U is the linear velocity of fluid flow, and L is the characteritic dimension of the reactor. 22. Define E( ) and F( ). Sketch E( ) vs. for (i) ideal PFR and (ii) ideal CSTR. The dimensionless function of exit age distribution E( ) is defined as E = t E = (V/M) C. Where t is the mean residence time, V is the volume of the reactor, M is the quantity of tracer, and C is the effluent concentration of tracer (by pulse input). The dimensionless form of C Step curve is called the F-curve. It is given by F = (v/m) C Step. Where v is the volume rate of flow of the reacting fluid, and m is the mass rate of flow of the tracer. Note: draw the E( ) vs. for ideal PFR and ideal CSTR. 23. What is tank s-in-series model? State its limitations. (Dec 2012) It is the model useful for representing flow in real vessels, for scale-up, and for diagnosing poor flow.it is simple, can be used with any kinetics, and it can be extended without too much difficulty to any arrangement if tanks, with or without recycle.this model is applicable only for not very viscous fluids, flowing in a pipe or tube. 24. Define peclet number. What is the value of peclet number for (i) ideal CSTR and (ii) ideal PFR. The reactor Peclet number (N Pe,R) is defined as the ratio of the rate of transport by convection to that of the rate of transport by diffusion or dispersion. It is given by N Pe,R = (U L)/D.Where U is the velocity of reacting fluid flow, L is the length of the reactor, and D is the dispersion or diffusion coefficient.for ideal CSTR, N Pe,R = 0 and for ideal PFR, N Pe,R =. 25. Define Schmidt number and Sherwood number The Schmidt number (N Sc) is defined as the ratio of the molecular momentum transfer to that of the molecular mass transfer. It is given by N Sc = μ/( d). Where d is the characteristic dimension of the reactor, is the density of the reacting fluid, and μ is the viscosity of the reacting fluid. The Sherwood number (NSh) is defined as the ratio of the total mass transfer to that of the molecular mass transfer. It is given by NSh = (kg d)/d.where d is the characteristic dimension of the reactor, k g is the mass transfer coefficient, and D is the diffusivity of the reactant. 26. Give Two examples for non ideal flow. (May2011) Short circuiting and formation of stagnant zones. 27. What are the models used to characterize non-ideal flow? (May 2015) The models for non-ideal reactors are Dispersion model Tank in series model Segregation model Compartment model 28. Define axial mixing and radial mixing. (Dec 2015) Axial (down and up) pumping is an important flow pattern because it addresses two of the most common challenges in mixing; solid suspension and stratification. In this process both the superficial and annular velocities can be calculated to determine and control the level of mixing Radial impellers are commonly selected for low level mixing (known as a tickler blade) or elongated tanks. They typically give high shear rates because of their angle of attack. They also have a relatively low pumping number, making them the most sensitive to viscosity. Radial impellers do not have a high tank turnover flow like axial flow impellers. 29. What are the factors which make up contacting in the reactor stream? (Dec 2015) VTHT 36

37 There are three interrelated factors make up the contacting or flow pattern: The RTD or residence time distribution of material which is flowing through the vessel The state of aggregation of the flowing material, its tendency to clump and for a group of molecules to move about together The earliness and lateness of mixing of material in the vessel. 30. Define selectivity for parallel reactions. (May 2016) Assume a reactant A which can form a desired product D, and an undesired side-product U in parallel reactions. moles of desired product formed (D) Selectivity = moles of undesired material formed (U) 31. Define tracer in RTD Studies. (May 2016) A tracer is a non-reactive chemical compound which will be introduced in the reactor feed stream in order to determine the flow patterns and exit age. Eg: Coloured dye PART-B QUESTIONS 1. Explain the different experimental methods for finding E-curve. (May 2013& Dec 15) Refer Octave Levenspiel notes page no: Explain C-curve, E-curve and F-curve. Derive the relation between them.(may 2013, 15) Refer Octave Levenspiel notes page no: The concentration reading in the table represents a continuous response to a pulse input into a closed vessel which is to be used as a chemical reactor. t, min C, gm/lit (i) Tabulate and plot the exit age distribution E. (ii) If the vessel used as a reactor for a liquid decomposing with rate -r A = k C A k = min -1, Find the fraction of reactant unconverted in the real reactor and compare this with the fraction unconverted in a PFR of the same size. (Dec-2004 & Dec-2005) VTHT 37

38 4. Write brief notes on reasons for deviations from ideal flow. Refer Octave Levenspiel notes page no: Discuss the Dispersion model and Tanks-in-series model to represent the non-ideality in real reactors. (May-2009& 2016) Refer Class Notes of Unit III 6. A small diameter pipe 32m long runs from the fermentationroom of a winery to the bottle filling cellar. Sometimes red wine is pumped through the pipe, sometimes white and whenever the switch is made from one to the other, a small amount of house blend is produced (8 bottles). Because of some construction in the winery, the pipe length to be increased to 50m. For the same flow rate of wine, how many bottles of red may we expect to get each time we switch the flow? (May-2009) Solution: Original : L 1 = 32m, σ 1 = 8 Longer Piper : L 2 = 50m, σ 2=? 7. Kerosene and gasoline are pumped successively at 1.1 m/s through a 25.5-cm ID pipeline 1000 km long. Calculate the 5195%-9515% contaminatedwidth at the exit of the pipe given that the kinematic viscosity for the 50150% mixture is μ ρ = m2 s (Data and problem from Sjenitzer, Pipeline Engineer, December 1958). VTHT 38

39 8. Assuming plug flow we calculate that a tubular reactor 12 m long would give 96% conversion of A for the second-order reaction A --+ R. However, the fluid is very viscous, and flow will be strongly laminar, thus we expect the convection model, not the plug flow model, to closely represent the flow. How long should we make the reactor to insure 96% conversion of A? (Dec 2011) 9. Fluid flows at a steady rate through 10 tanks in series. A pulse of tracer is introduced into the first tank, the time this tracer leaves the system is measured giving. Maximum concentration =100 mmol/lit, tracer soread = 1 min, if 10 more tanks are connected in series with the original 10 tanks what would be (i) the maximum concentration of leaving tracer? (ii) The tracer spread? (iii) How does the relative spread change with number of tanks? (May 2012) VTHT 39

40 10. (i) Discuss the effects of non-ideal with examples. (Dec 2012) (ii) Explain the methods of conducting stimulus responses experiments with various inputs. Refer Class Notes 11. From a pulse input in to a vessel, the following output signal is obtained. Time (t) Conc. (g/l) This has to be represented the flow through the vessel with tank-in-series model. Using the variance matching procedure, determine the number of tanks in use. Also, calculate the vessel dispersion number (D/UL). (May 2013) 12. Aqueous A (C AO = 50 mol/m 3 ) with physical properties close to water (ρ = 1000 kg/ m 3, Diffusivity = 10-9 m 2 /s) reacts by a second order reaction (k = 10-3 m 3 / mol.s) as it flows at 10 mm/s through a tubular reactor (d t = 10 mm, L = 20 m). Find the conversion of reactant A from this reactor. 13. A liquid reactant stream with C A0 = 1 mol/lit passes through two CSTR in series. The concentration of A in the stream leaving the first reactor is 0.5 mol/lit. Find the concentration of A in the exit stream for the second reactor. The reaction is second-order with respect to reactant A and the volume of the second reactor in series twice that of the first reactor. (May 2015) 14. An aqueous reactant stream with C A0 = 4 mol/lit passes through a mixed flow reactor followed by a plug flow reactor. Determine the concentration at the exit of the plug flow reactor if C A = 1 mol/lit in the mixed reactor. The reaction is second order with respect to A and V plug/v mixed = 3. (May 2015) VTHT 40

41 15. The concentration reading given below represents a continuous response to a pulse input in to a closed vessel. (Dec 15) Time (t) C pulse(g/m 3 ) This vessel is to be used as a reactor for decomposition of liquid A. the reaction kinetics and stoichiometry are given by A Products, r A = kc A, k = 0.10 min -1. Calculate the conversion of reactant A in the real reactor. 16. A reactor has the flow characteristics given by the non-normalized C-Curve in table below and by the shape of this curve; we feel that the dispersion on tank-in-series model should satisfactorily represent flow in reactor. (May 2016) Time (t) Conc. (g/l) i) Find the conversion expected in the reactor, assuming that the dispersion model holds good. ii) Find the number of tank-in-series which will represent the reactor and the conversion expected, assuming that tank-in-series holds well. iii) Find the conversion by direct use of tracer curve given X A = 99% for a PFR. VTHT 41

42 VTHT 42

43 UNIT-IV GAS-SOLID, GAS-LIQUID REACTIONS PART-A QUESTIONS & ANSWERS 1. List the sequence of steps involved in heterogeneous processes. The sequence of steps involved in heterogeneous processes is; Transport of reactants from the bulk fluid to the fluid-solid interface. Intra-particle transport of reactants into the catalyst particle (if it is porous). Adsorption of reactants at interior sites of the catalyst. Chemical reaction of adsorbed reactants to adsorbed products (surface reaction - the intrinsic chemical step. Transport of products from the interior sites to the outer surface of the catalyst particle. Transport of products from the fluid-solid interface into the bulk-fluid stream. 2. Give the types of heterogeneous reactions. The types of heterogeneous reactions are; Gas-Solid catalytic reactions (Hydrocarbon transformations) Gas-Solid non-catalytic reactions (combustion reactions) Gas-Liquid-Solid reactions (Hydrogenation reactions) Gas-Liquid reactions (Absorption) 3. List the advantages of the Langmuir-Hinshelwood method in developing rate equations. The advantages of the Langmuir-Hinshelwood method are; The resultant rate equation may be extrapolated more accurately to concentrations beyond the range of experimental measurements used. The method does take into account adsorption and surface reactions (which must occur) in a consistent manner. 4. What is the effect of intrapellet heat transfer? The effect of intrapellet heat transfer (temperature gradient) is to increase the rate for an exothermic VTHT 43

44 reaction. This is because intrapellet temperatures will be greater than surface values. For endothermic reactions, both temperature and concentration gradients reduce the rate below that evaluated at outersurface conditions. 5. When bulk and Knudsen diffusion occurs? Bulk diffusion occurs when the pores of a solid catalyst are considerably large and the gas is relatively dense or if the pores are filled with liquid. If the pore size of a solid catalyst is small and as the gas is less dense, then in such cases, molecules collide more frequently with the catalyst pore walls as compared to collisions among each other. This type of diffusion phenomena is called Knudsen diffusion. 6. Write short notes on surface diffusion. The transport by movement of adsorbed molecules over the catalyst surface is called Surface Diffusion. The direction of diffusion is that of the increasing surface concentration. Surface diffusion contributes little to overall transport through a porous mass unless appreciable adsorption occurs. 7. What do you mean by effective diffusivity? In a porous catalyst the pores in a catalyst are not straight and they follow tortuous, interconnecting paths having varying cross sectional area. To account this variation, effective diffusivity is considered. Effective diffusion coefficient accounts for the average diffusion taking place at any position in the catalyst pellet. 8. Define effective thermal conductivity. The effective thermal conductivity (k e) is the energy transferred per unit of total area of pellet (perpendicular to the direction of heat transfer). 9. Define effectiveness factor. The effectiveness factor (η) is defined as the ratio of actual rate for the whole pelletto the rate evaluated at outer surface conditions. 10. Write the expression for Thiele modulus with respect to spherical catalyst. Thiele modulus for spherical catalyst is Ф s = r s/ 3 (k p / D e) 1/2 Where r s - Radius of the spherical catalyst k - First order reaction rate constant p - Density of the catalyst pellet;d e - Effective diffusivity 11. Write the expression for effectiveness factor for a single cylindrical pore on the catalyst. The effectiveness factor for a single cylindrical pore on the catalyst pellet (in which first orderreaction occurs) is η = tanh (Ф L) / Ф L Where Ф L is the Thiele modulus and is given by Ф L = L / (k 1 p / D e) 1/2 L is the thickness of cylindrical pore. 12. Give the industrial importance of Gas-Solid non-catalytic reactions. (Dec 2012) Gas-Solid non-catalytic reactions are employed in; Roasting of ores. The preparation of metals from their oxides in reducing atmospheres. The platting of metals. Reactions of carbonaceous materials. 13. List the sequence of steps involved in determining the global rate for an irreversible Gas-Solid non-catalytic reactions. For an irreversible Gas-Solid non-catalytic reaction, the global rate will be determined by the four steps; Mass transfer from bulk fluid to the outer surface of the particle. Intra-particle diffusion into the particle. Adsorption at an active site of solid reactant. Intrinsic (surface) reaction at the site. 14. List the models explained for Gas-Solid non-catalytic reactions. For the Gas-Solid non-catalytic reactions, the two idealized models are; Progressive-conversion model Shrinking-core model 15. Compare the Progressive-conversion and Shrinking-core model. Progressive-conversion model: VTHT 44

45 Solid reactant is converted continuously and progressively throughout the particle. The reaction rates are different at different locations within the particle. This model does not match with the real situations. Shrinking-core model: At any time there exists an unreacted core of material which shrinks in size during reaction. The reaction rate depends on the movement of unreacted core and the resistances involved in it. Most of the practical situations (burning of coal, wood, briquettes, etc.) show that this model approximately matches with reality. 16. List the steps occurring in the development of shrinking-core model. Consider the non-catalytic reaction A(g) + b B(s) Products. The five steps occurring in the development of shrinking-core model are; Diffusion of gaseous reactant A through the film surrounding the particle to the surface of the solid. Penetration and diffusion of A through the blanket of ash to the surface of the unreacted core. Reaction of gaseous A with solid at this reaction surface. Diffusion of gaseous products through the ash back to the exterior surface of the solid. Diffusion of gaseous products through the gas film back into the main body of fluid. 17. What are the assumptions made over shrinking-core model? The assumptions made in the development of shrinking-core model are; The pellet retains its shape during reaction. There is no gaseous region between the pellet and the product layer. The temperature is uniform throughout the heterogeneous region. The densities of the porous product and the reactant (solid) are the same, so that the total radius of the pellet does not change with time. 18. What are the various controlling regimes in a fluid-solid non-catalytic reaction? (May 2012) The various controlling regimes in a fluid-solid non-catalytic reaction are; Gas film, surrounding the solid particle in which diffusion of gas takes place. Product layer, in which diffusion of gas takes place for further formation. Reaction zone, which takes place at the interface. 19. Write the expression of the time for complete conversion in shrinking core model for spherical particles, when diffusion through gas film controls. The time for complete conversion ( ) of a spherical particle in shrinking core model, when diffusion through gas film controls, is = B R / 3 b k gc Ag Where B - Molar density of the solid (B), moles of B / m 3 solid R - Radius of the solid particle, m b - Moles of B reacted, according to stoichiometry C Ag - Bulk gas concentration, moles of A / m 3 k g - Gas film mass transfer coefficient, m/sec 20. Write the expression of the time for complete conversion in shrinking core model for spherical particles, when diffusion through ash (product) layer controls. The time for complete conversion ( ) of a spherical particle in shrinking core model, when diffusion through ash layer controls, is = B R 2 / 6 b D ec Ag Where B - Molar density of the solid (B), moles of B / m 3 solid R - Radius of the solid particle, m b - Moles of B reacted, according to stoichiometry C Ag - Bulk gas concentration, moles of A / m 3 D e - Effective diffusivity, m 2 /sec. 21. Write the expression of the time for complete conversion in shrinking core model for spherical particles, when chemical reaction controls. The time for complete conversion ( ) of a spherical particle in shrinking core model, when chemical reaction controls, is = B R / b k C Ag Where B - Molar density of the solid (B), moles of B / m 3 solid R - Radius of the solid particle, m b - Moles of B reacted, according to stoichiometry C Ag - Bulk gas concentration, moles of A / m 3 VTHT 45

46 k - Net reaction rate constant, m/sec. 22. What are the limitations of the shrinking core model? (May 2016) It is the best simple representation for the majority of reacting gas-solid systems. However, there are two broad exceptions to this statement. First, Slow reaction of a gas with a very porous solid will not fit to the reality; Second, when solid is converted by the action of heat and without needing contact with gas Such as baking bread, roasting chickens are examples of such reactions. 23. Write how the rate determining step is determined with the help of particle size. The kinetic runs with different sizes of particles can distinguish between reactions in the chemicaland physical steps control as, 1.5 to 2.0 t R for film diffusion controlling t R 2 for ash diffusion controlling t R for chemical reaction controlling. 24. List the various types of contacting pattern in gas-solid operations. The various types of contacting pattern in gas-solid operations are; Solids and Gas both in plug flow (Blast furnace, Moving grate reactor, Rotary dryer) Solids in mixed flow (Fluidized bed reactor) Semi batch operations (Ion-exchange operations) Batch operations ( Acid attack of a solid) 25. Write the expression for mean conversion of mixture of solids, unchanging sizes, in the plug flow of solids. The expression for mean conversion of mixture of solids, unchanging sizes, in the plug flow of solids is R m 1 X B = [1 X B(R i)] F(R i)/f R(t p=τ) Where R m - Radius of the largest particle in the mixture R(t p = ) - Radius of the largest particle completely converted in the reactor. X B(R i) - Conversion for any size of particles R i F(R i) - Quantity of material of size about R i fed to the reactor F - Quantity of solid being treated. 26. What is mass transfer resistance? (Dec 2012) The resistance to mass transfer is defined as the reciprocal of the mass transfer coefficient [ 1 k x ], Represents the resistance to mass transfer in the liquid phase. [ 1 k y ], Represents the resistance to mass transfer in the gas phase. It is important to know if one of the 2 resistances is controlling the mass transfer. If so, the rate of mass transfer can be increased by promoting turbulence in and/or increasing the dispersion of the controlling phase. 27. What is the physical significance of Thiele modulus? (May 2013) Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets. The Thiele modulus is represented by different symbols in different texts, but is defined in diffusion time h T = reaction time 28. Draw the energy diagram of catalyzed and Uncatalyzed reaction. (May 2014) VTHT 46

47 29. What is the pore resistance limits for porous catalytic particles? (May 2015) When reactant fully penetrates the particle and bathes all its surfaces, then the particle is in the diffusion free regime. This occurs when MT<0.4 or MW<0.15. At some extreme when the centre of the particle is starved for reactant and is unused then the particle is in the strong pore resistance regime. This occurs when MT>4 or MW> Define Damkohler Number. (May 2016) The Damköhler numbers (Da) are dimensionless numbersused in chemical engineering to relate the chemical reactiontimescale (reaction rate) to the transport phenomena rate occurring in a system. Reaction rate Diffusion time Da = = Diffusion rate Reaction time Da is associated with characteristic diffusion and reaction times therefore scaling is necessary. For Da >>1 the reaction rate is much greater than the diffusion rate distribution is said to be diffusion limited (diffusion is slowest so diffusion characteristics dominate and the reaction is assumed to be instantaneously in equilibrium) For Da <<1 diffusion occurs much faster than the reaction, thus diffusion reaches an equilibrium well before the reaction is at equilibrium. 31. Describe the features of random pore model. (May 2016) For fluid-solid reactions, a random pore model is developed which allows for arbitrary pore size distributions in the reacting solid. The model can represent the behavior of a system that shows a maximum in reaction rate as well as one that does not, and it identifies an optimal pore structure for either of such systems. PART-B QUESTIONS 1. What do you understand by Thiele modulus and Effectiveness Factor for catalyst particles? 2. The catalytic reaction A 4R is run at 3.2 atm and 117 C in a plug flow reactor which contains 0.01 kg of catalyst and uses a feed consisting of the partially converted product of 20 liters/hr of pure unreacted A. The results are as follows: Run C Ain, mol/lit C Aout, mol/lit Find a rate equation to represent this reaction. (May 2015) VTHT 47

48 3. Determine the amount of catalyst needed in a packed bed reactor for 75% conversion of 1000 mol A/min of a C A0 = 8 mol/m3 feed. VTHT 48

49 4. Derive the rate expression for finding out effectiveness factor for spherical catalyst particle. Assume first order irreversible reaction takes place on the catalyst. 5. Derive the equation to find out conversion for particle of unchanging in size, when ash layer and chemical reaction controls the rate of reaction. Assume unreacted core model. (May 09, 16, Dec 12) 6. A batch of solids of uniform size is treated by gas in a uniform environment. Solid is converted to give a non-flaking product according to the shrinking-core model. Conversion is about 7/8 for a reaction time of 1 hr, conversion is complete in two hours. What mechanism is rate controlling? VTHT 49

50 7. Explain the parameter used to identify the kinetic regimes in Fluid-Fluid reactions and how is it used? 8. A first order reaction takes place between species A (in gas phase) and species B (in liquid phase). The reaction is fast. Derive the overall rate expression. 9. Derive the rate equation for fluid-fluid reaction for the following cases; (i) Instantaneous reaction with low and high C B (ii) Fast reaction with low and high C B 10. For the reactiona (g) + bb (s) cc (g) + dd (g) described by unreacted core model when ash layer is the rate controlling step for particles of unchanging size, establish the relationship between conversion and time. (May 2013) 11. A feed consisting of, 30% of 50 μm- radius particles, 40% of 100 μm-radius particles, 30% of 200 μm-radius particles, is to be fed continuously in a thin layer onto a moving grate cross current to a flow of reactant gas. For the planned operating conditions, the time required for complete conversion of solids to the grate for a residence time of 8 min in the reactor. (May 2013) 12. Describe pore diffusion resistance combined with surface kinetics. (May 2015) 13. Derive the rate equation for two resistances in series to transfer A from gas to liquid.(dec 2015) 14. Derive the equation for resistance in series in the G/L reaction on a catalyst surface.(dec 2015) UNIT-V- FIXED BED AND FLUID BED REACTORS PART-A QUESTIONS & ANSWERS 1. When the heterogeneous fluid-fluid reactions take place? Heterogeneous fluid-fluid reactions are made to take place for one of the three reasons; The product of reaction may be a desired material. To facilitate the removal of an unwanted component from a fluid. To obtain a vastly improved product distribution. 2. Give the importance of equilibrium solubility in gas-liquid operations. The solubility of the reacting components will limit their movement from one phase to other. This factor will certainly influence the form of the rate equation since it will determine whether the reaction takes place in one or both phases. 3. What is the assumption made on gas-liquid reactions while developing rate equation? The assumption is that gaseous A is soluble in the liquid B but B does not enter into the gas. Thus, A must enter and move into the liquid phase before it can react, and reaction occurs in this phase alone. 4. On what factors the special forms of rate equations depends? All sorts of special forms of the rate equations depends on the relative values of the rate constant (k), the mass transfer coefficients (k g and k l), the concentration ratio of reactants (p A/C B), AND Henry s law constant (H A). VTHT 50

51 5. Write the general rate equation for gas-liquid reactions. The general rate equation for gas-liquid reactions is -r A = p A / [ (1/ k Aga) + (H A / k Ala E) + (H A / kc Bf l) ] Where 1/ k Aga gas film resistance H A / k Ala E liquid film resistance H A / kc Bf l bulk liquid resistance 6. Define Enhancement factor. The liquid enhancement factor (E) is defined as E = (Rate of take up of A when reaction occurs / Rate of take up of A for straight mass transfer) at same C Ai, C A, C Bi, C B in the two cases.e is always greater than one or equal to one. 7. Define Hatta number. Give its significance. (May &Dec 2015) Hatta number (M H) is defined as the square root of the ratio of maximum possible conversion in the film to maximum diffusional transport through the film. The significance of Hatta number (M H) is; If M H>2, reaction occurs in the film and are fast enough. If 0.02 < M H< 2, reaction is influenced by all the resistances. If M H< 0.02, reactions are infinitely slow. 8. Write the expression which relates the partial pressure and concentration of a soluble gas in the absorption tower. At any point, say 1 and 2, the expression which relates the partial pressure and concentration of a soluble gas in the absorption tower is p A2 p A1 = (F l / F g C T) (C A2 C A1) Where F l - molal flow rate of all liquids; F g - molal flow rate of all gases. - Total pressure of the system; C T - molar density of the liquid. 9. What do you mean by instantaneous reactions in the gas-liquid operations? In instantaneous reactions, the absorbing component of the gas and the liquid phase reactant cannot co-exist in the same region. In such reactions, the concentration of the liquid phase reactant at the gas-liquid interface is zero. 10. What do you mean by fast reactions in the gas-liquid operations? In fast reactions, reaction is fast enough so that the reaction zone remains totally within the liquid film. Thus, no gas phase reactants enter the main body of liquid to react there. 11. What do you mean by slow reactions in the gas-liquid operations? In slow reactions, occurs in the main body of the liquid, mass transfer resistance isnegligible and the composition of liquid phase and gas phase reactants are uniform. Thus, the rate is determined by chemical kinetics alone. 12. In what way the chemical reactions help in gas-liquid operations? In general, reaction lowers the resistance of the liquid film. So, For absorption of highly soluble gases, chemical reaction doesn t enhance the rate. For absorption of slightly soluble gases, chemical reaction is helpful, and enhances the rate. 13. Write short notes on slurry reactors. (May2011) A slurry reactor is a multiphase flow reactor in which reactant gas is bubbled through a solution containing solid catalyst particles. The solution may be either a reactant or a product or an inert. Slurry reactors may be operated in a batch or continuous mode. One of the main advantages of slurry reactors is that temperature control and heat recovery are easily achieved. In addition, constant overall catalytic activity can be maintained by the addition of small amounts of catalyst with each reuse during batch operation or with constant feeding during continuous operation. These reactors are widely used in hydrogenation of fatty acids over a supported nickel catalyst, hydro-formation of CO with high-molecular-weight olefins on either a cobalt or ruthenium complex bound to polymers, etc. 14. Write short notes on trickle bed reactors. A trickle bed reactor is a three-phase version in which gas and liquid reactants are brought into contact with solid catalyst particles. In this gas and liquid flow counter-currently downward over a fixed-bed of catalyst particles contained in a tubular reactor. These reactors are widely used for hydro-desulphurization of liquid petroleum fractions and hydrotreating of lubricating oils. 15. List the types of flow regime that are possible in trickle bed reactors. VTHT 51

52 In trickle bed reactor, four types of flow regimes are possible; Trickle flow regime: In this regime, gas flow is continuous. Dispersed bubble regime: In this regime, liquid phase is continuous and the gas moves into the bubbles. Spray regime: In this regime, gas flow rate is high while liquid rate is low. Liquid falls in droplets through the gas phase. Pulsed flow regime: In this regime, flow rates of both gas and liquid are high. 16. Compare fixed and fluidized - bed reactors. (May 2013) (i) It is not possible to use fine size catalyst particles in fixed bed reactor. This results in plugging and high pressure drop. High pressure increases theoperating cost.it is possible to use fine size catalyst particles in fluidized bed reactor. Fine size particles provide large interfacial / contact area. (ii) Catalyst regeneration can be a problem in fixed bed reactor. If the regeneration needs to be frequently done, this problem will be bottleneck in operation. Catalystparticle regeneration is quite easy in fluidized bed reactors. If the regeneration needs to be done frequently, the catalyst particles can be entrained with the product stream, separated in cyclone separator and then sent to the regenerator. 17. Write the expression for mean conversion of single solid, unchanging sizes, in the mixed flow of solid. The expression for mean conversion of single solid, unchanging sizes, in the mixed flow of solids is 1 - X B = (1 - X B) ind. par (e -t/t /t) dt 0 Where (1 - X B) ind. par. - Fraction unconverted, depends on the various controlling regimes. - Time for complete conversion t - Mean residence time. 18. Write the expression for mean conversion of mixture of solids, unchanging sizes, in the mixed flow of solids. The expression for mean conversion of mixture of solid, unchanging sizes, in the mixed flow of solids is R m 1 X B = [1 X B(R i)] F(R i)/f R=0 Where 1 - X B(R i)- Fraction unconverted of individual particles, depends on the various controlling regimes. F(R i) - Quantity of material of size about R i fed to the reactor F - Quantity of solid being treated. R m - Radius of the largest particle in the mixture 19. List some of the problems in operation of a fluidized catalytic reactor. In operation of a fluidized catalytic reactor, some difficulties can occur. They are; Slugging: When the gas passes up through the catalyst bed in the form of large gas bubbles, it is called as Slugging of fluidized bed. Channeling: When the gas is not evenly distributed in the catalyst bed cross section and is concentrated in channels through the catalyst bed, the phenomena is called as Channeling of fluidized bed. 20. State the sequence of steps involved in the overall reaction process for G/L reactions on solid catalyst. The general reaction stoichiometry for G/L reactions on solid catalyst is on catalyst surface A (g l) + b B (l) Products. Here the gas phase reactant first dissolves in the liquid and then both reactants (A & B) move on the catalyst surface for reaction to occur. For reactant A the following steps are involved in the overall reaction process; Transport from the bulk gas to the G/L interface through the gas film Transport from the G/L interface to the bulk liquid through the liquid film Transport from the bulk liquid to external catalyst surface through the liquid film surrounding the particle.diffusion and reaction within the porous catalyst particle 21. What do you mean by three phase fluidized bed reactor? (May 2013) VTHT 52

53 It is a heterogeneous reactor in which solid (S) is fluidized by the gas (G), on top of it liquid (L) is sprayed counter-currently. The performance of it varies widely in G/L ratio from gas (G) bubbling through an liquid (L) slurry to a gas (G) fluidized bed of damp solid (S) particles and it lies between the performances of slurry and trickle bed reactors. 22. On what factors the selection of contactor for G/L reactions on solid catalyst depends? The selection of good contactor for G/L reactions on solid catalyst depends on; Where the controlling resistance lies in the rate expression, The advantages of one contacting pattern over another, and The difference in auxiliary equipment needed. The overall economics which accounts for these three factors will determine which set up and reactor type is best. 23. List the industrial applications of reactors for G/L reactions on solid catalyst. The catalytic hydrogenation of petroleum fractions to remove sulfur impurities. The catalytic oxidation of liquid hydrocarbons with air or oxygen. The removal of dissolved organics from industrial waste water by catalytic oxidation as an alternative to bio-oxidation.the removal of airborne pollutants by adsorption and/or reaction. 24. Write short notes on Reactors for Fluid-Fluid reactions. (May2011) The reactor for Fluid-Fluid (Gas-Liquid) reactions is named as Double mixed reactor. The particular features of this reactor are; Mixed flow of gas and of liquid, hence uniform composition in the bulk of each phase. The agitation rate in the phase can be changed independently. The surface to volume ratio can be varied by changing the interfacial contact area. The concentration level of reactants can be raised or lowered by changing the feed rate or feed composition. Because of mixed flow of the phases the rate of absorption and reaction can be found directly by means of a material balance. 25. Define Jet impact factor. (May 14) The idea here is to force two streams, one of reactant, the other of a very hot heat carrier or catalyst, to collide at very high velocity and thereby mix intensely and react at high temperature. For an all-gas product, the product stream is rapidly quenched, while for a gas-solid product, a cyclone separates the two phases, after which the gas is rapidly cooled. By using the word "rapidly" we mean that the whole operation-mixing, reacting, separating and quenching-is done in 0.1 to 0.3 seconds 26. Give three examples of non catalytic reactions. (May2011) 1. Addition of hydrogen to maleic acid. 2. Reaction of isonitriles 3. Reaction of carboxylic acids 27. What is pulse input? (May 2015) In a pulse input, an amount of tracer is suddenly injected in one shot into the feed stream entering the reactor in as short time as possible for RTD analysis.. The outlet concentration is then measured as a function of time. Theconcentration-time curve is referred to as the C curve. 28. Write the significance of fixed bed reactor. (Dec 2015) Fixed-bed reactors have long been used in process industries and they contain catalyst, typically in pellet form, packed in a static bed. The syngas is then passed through the bed, where the reactions are induced as the gases contact the catalyst. Originally, fixed-bed reactors were the only commercially viable reactor. 29. What are the characteristics of fluidized bed reactor? (May 16) They consist of a bed of immobilized enzyme which is fluidized by the rapid upwards flow of the substrate stream alone or in combination with a gas or secondary liquid stream, either of which may be inert or contain material relevant to the reaction. A gas stream is usually preferred as it does not dilute the product stream. There is a minimum fluidization velocity needed to achieve bed expansion, which depends upon the size, shape, porosity and density of the particles and the density and viscosity of the liquid. This minimum fluidization velocity is generally fairly low (about 0.2 -I.0 cm s-1) as most immobilized-enzyme particles have densities close to that of the bulk liquid VTHT 53