CHEMICAL KINETICS CLASS XII

Transcription

1 CHEMICAL KINETICS CLASS XII

2 Introduction Chemical reactions deal with change in either reactants or products. They involve processes by which substances with distinct properties are transformed into one or several products with new properties. Everyday experience tells us that chemical reactions take place in various ways. Some reactions are so rapid that they occur as soon as the reactants are mixed. For example, the immediate addition of oxygen to the blood forming oxyhemoglobin as we inhale air and its conversion to carbon dioxide as we exhale. Some other reactions are so slow that they are unnoticed; for instance, the rusting of iron in summer is so slow that it can mislead into thinking that no reaction is taking place at all. Chemical kinetics is the branch of chemistry that concerns with the rate of chemical reactions and the mechanisms that control it. When a chemist needs to know whether a chemical reaction is feasible or not under certain conditions, he needs to look at the 'thermodynamics' of the chemical reaction. If he needs to know the extent a reaction can proceed or whether it can progress to equilibrium or not he will study the thermodynamics of its chemical equilibrium. But when it is important to understand how rapidly or slowly a chemical change occurs and the parameters that control the rate of the chemical reaction one turns to the study the chemical kinetics of a reaction. The study of chemical kinetics is important as it has wide ranging applications in the modern day world - from economical industrial production of chemicals to mechanism of transformation of drugs in the human body. How does one increase the effectiveness of drugs during critical phases of disease... or make faster setting cement in areas where water availability is a problem? Is there a way to speed up the process of cheese formation or find ways to retard the effect of food spoiling? Can one slow down or stop the

3 effects of chemical pollutants in the environment? Chemical kinetics has come along way since the first chemical reaction, the hydrolysis of sucrose, was quantitatively studied by L. Wilhemly in Many advances have been made in this field since then, enabling chemists to study reactions that occur within less than a second. The precipitation of silver chloride to create photographic../content/cb12c1/content/topic/ch724/images is one such instance. Such advances have enabled chemists to discover intermediates in many elementary reactions and thereby propose mechanisms of complex reactions. Many reactions, however, proceed at conveniently measurable times, and their rates can be measured easily, for example, the reaction between nitrogen dioxide and carbon monoxide or the decomposition of hydrogen peroxide. In this chapter, one studies the speed or rate of a chemical reaction together with the rates of consumption or formation of substances and the amounts reacted or formed. Chemical kinetics also describes the conditions by which the reaction rates are altered. Factors such as concentration, temperature, pressure and catalysts affect the rate of a reaction. At the molecular level, the reaction mechanisms involving orientation and energy of molecules undergoing collisions will also be discussed. Rate of a Chemical Reaction Chemical reactions involving ionic species, known as ionic reactions, are very fast. For example, Precipitation of silver chloride occurs very quickly on mixing the solutions of silver nitrate and sodium chloride. Acid-base neutralization occurs instantaneously as soon as the two

4 substances are mixed in their aqueous solutions. These reactions occur in about to seconds and are extremely fast. On the other hand, certain reactions can occur at an exceedingly slow speed. For example, a mixture of carbon and oxygen at room temperature remains un-reacted even for years. That is why coal is stored safely in contact with oxygen of the air. The speeds of the above types of reactions cannot be measured easily because they are either too fast or too slow. In between these two extremes, there are many reactions that occur in conveniently measurable times and their speeds can be measured easily. For example: The reaction between nitrogen dioxide and carbon monoxide Decomposition of hydrogen peroxide These reactions, which proceed at conveniently measurable speeds, are of interest to chemists for the better understanding of their mechanisms. Nevertheless, modern techniques have been developed which are used to study even extremely fast reactions. Just as the speed of an automobile is expressed in terms of the change of its position or distance traveled by it in a certain period of time, the speed of a reaction determines how fast or slow the reactants are converted into products. An idea about the rate of a reaction can be obtained by observing either the speed of disappearance of the reactants or the speed of appearance of the products. For example: when a piece of magnesium is put into a beaker containing dilute hydrochloric acid, hydrogen gas evolves rapidly and magnesium disappears at once. On the other hand, when a piece of iron is placed in the same acid, hydrogen gas evolves at a considerably slower rate and iron also

5 disappears very slowly. By observing the speed at which reactants disappeared or product formation took place one can discern that the reaction of magnesium with hydrochloric acid is much faster than the reaction of iron and hydrochloric acid. The speed at which a given reaction occurs essentially refers to the rate at which the reaction takes place. In chemical reactions the speed of a reaction is determined by monitoring the concentrations of the reactants or products at intervals of time. The volume of the reaction vessel is kept constant and there is no addition to or removal of any of the reactants and products from the reaction vessel. For a hypothetical reaction, as the reaction proceeds the concentration of the reactant (A) decreases with time while the concentration of the product (B) increases. If the concentration of the reactant (A) is monitored at different times, say t 1 and t 2 then the rate of the reaction (r) is given as, r = Rate of disappearance of A If the product [B] is monitored then the rate of the reaction is given by r = Rate of appearance of B

6 Average Rate of a Reaction The average rate of a reaction is defined as the rate of change of concentration of a reactant or a product over a specified measurable period of time. This can be calculated by dividing the concentration difference by the given time interval. Considering the above reaction, if [A] 2 is the concentration of reactant A at time t 2 while [A] 1 is the concentration reactant A at a time t 1 then average rate (r) is The square brackets are used to express molar concentration. Equation 1 can be written as, Δ [Α] signifies the change in concentration of A, while 'Δt' is the time interval. Similar to the above, with [B] 2 as the concentration of product B at time t 2 and [B] 1 as the concentration product B at a time t 1, then the average rate in terms of B is, Equation 3 can be written as, Equations (2) and equation (4) represent the average rate of a reaction. For the hypothetical reaction, the rate of the reaction in the terms of appearance and disappearance of the product and reactant is given as,

7 The average rate of a reaction is a positive quantity. As a negative sign precedes the term in the equation of the rate of reaction when expressed in terms of concentrations of the reactants, it is always multiplied with -1 to express it as a positive quantity. When the concentration of the reactant or product is plotted with time on a graph, it is clear that the rate of reaction actually decreases with time. This is because the rate of reaction depends on the concentrations of the reactant, which get progressively used up as the reaction proceeds to completion.

8 The average rate is the change in concentration of reactants or products and the time taken for that change to occur. It is given by a straight line between two points of the curve in the graphs. The instantaneous rate is the change in concentration of reactants or products taking place at that moment of time and is given by the slope of the curve. Both these lines become flatter as we move to the right (time increase) indicating a slowing down of the rate of reaction. The units of rate are concentration time -1. When concentration is expressed in mol L -1 and time in seconds then the units will be mol L -1 s -1. In gaseous systems the units of the rate equation is atm s -1 as the concentration of gases is expressed in terms of their partial pressures. Example: The gaseous phase decomposition of dinitrogen pentoxide (N 2 O 5 ) to nitrogen dioxide (NO 2 ) and oxygen (O 2 ) is given by,. For the reaction the concentration of O 2 was monitored and the following data were obtained. Time (s)

9 [O 2 ] in M Calculate the average rate of reaction. Solution: The average rate of reaction is calculated by determining the difference in [O 2 ] concentration over different intervals of time and dividing the difference by Δ t, [O 2 ] 1 [M or mol L -1 ] [O 2 ] 2 [M or mol L -1 ] t 2 (s) t 1 (s) x x x x x 10-7 From the above data it is obvious that the average rate of reaction decreases with time. Within the time interval of 0 to 3000s, the average rate of the reaction falls by a factor of four. Hence, Average rate of reaction is not constant but decreases with time, reaching a value of zero when the reaction is complete. This occurs as the rate of reaction depends on the concentration of one or more reactants. Accordingly, when concentration of a reactant decreases, the rate of the reaction also decreases. The rate of the reaction changes with time, therefore, the rate that we measure depends on the time interval used.

10 Instantaneous Rate of a Reaction The average rate of a reaction does not represent the actual rate of a reaction. Since the concentration of the reactant is continuously decreasing, it makes sense, to express the rate of a reaction at a particular instant of time. Average rate is measured over a time interval Δ t. When this time interval is infinitesimally shortened, that is, then the average rate equation becomes the expression for instantaneous rate (r inst ). Instantaneous rate of reaction is defined as the rate of change of concentration of any one of the reactants or products at a given time. To measure the instantaneous rate the time interval ' t' should be made as small as possible so that there is the least possible change in rate over that interval. Such rates may be represented in terms of infinitesimally small change in concentration of reactant or product (written as d[x]) in infinitesimally small interval of time, 'dt'. The rate of the reaction may be expressed as: If the rate is expressed in terms of concentration of any one of the reactants, which keeps on decreasing, the negative sign is used. On the other hand, if the rate of the reaction is expressed in terms of the concentration of any one of the products which goes on increasing, it is a positive value. Mathematically, instantaneous rate (r inst ) for the reaction is given by, Instantaneous rate is the value of for the tangent at a given time 't'. In terms of the concentration versus time curves of the reactants and the products shown earlier, it is actually the slope of the tangent.

11 r inst = -slope for the reactant = + slope for the product Example: Dehalogenation of trimethyl bromide (CH 3 ) 3 CBr is given by the reaction. The following data were obtained. Time (hr) [(CH 3 ) 3 CBr] x 10-2 M Calculate the instantaneous rate by plotting the data as concentration versus time and taking the slope of the tangent drawn to the curve at some point of time 't'. Solution The plot of concentration versus time is shown in figure below. The rate of the reaction at a particular time is determined by drawing a tangent to curve at a point corresponding to that time. Then the slope of the tangent gives the rate of the reaction at that time.

12 The instantaneous rates were calculated at times 6.5 hours and 16.2 hours. The rates are, At time 6.5 hours = 0.39 M / hr At time 16.2 hours = 0.23 M / hr From the above data it is observed that the instantaneous rate appear to change with time. Expressions of Rates of Reaction The amounts of reactants and products in a chemical reaction are related by stoichiometry. Therefore, the concentration of any reactant or product can be used to express the rate of a reaction. For example: In the reaction, For every molecule of A consumed, a molecule of B is also consumed and thereby a molecule of C, the product, is formed. Hence, the rate of a reaction can be expressed as,

13 Where the stoichiometric coefficients of the reactants and products are same then the rate of disappearance of any of the reactants is same as the rate of appearance of the products. But when the stoichiometric coefficients of reactants or products are not equal to one another then the expression is different. For a reaction of the type, the rate expression changes. For every molecule of A consumed, two molecules of B are required to form one molecule of C and two molecules of D. In other words, the concentration of B changes at twice the rate of change of concentration of A, while the concentration of D increases at two times the rate of decrease of A. Therefore, the rate of reaction is given by, In such cases the rate of disappearance of any of the reactants or the rate of appearance of products is divided by their respective stoichiometric coefficients. From the above example, it is also clear that the rate of a reaction has no meaning unless it is measured with respect to a particular species in the reaction. Example: Express the rate of the reaction given, in terms of reactants and product concentrations. Solution The rate of the reaction is expressed as, Since all are gaseous species here the concentration is directly proportional

14 to the partial pressure of the species and hence, rate can be expressed as rate of change in partial pressure of the reactant or the product. Experimental Determination of Rate of Reaction The rate of a reaction is determined by measuring the concentration of the reactant or product at different intervals of time. The concentration is measured, by measuring a related property such as colour, pressure or volume (as in the case of gas phase reactions), ph, optical rotation, electrical conductivity and thermal conductivity. For liquid phase reactions, a small amount of the reaction mixture is withdrawn and the reaction is stopped either by quenching the reaction with a suitable solvent, or freezing the sample in a freezing mixture. This method is repeated with all the samples that are collected at different intervals of time. Then the concentrations in the samples are determined with a suitable analytical technique that monitors any of the properties mentioned above. For example, hydrolysis of ethyl acetate in acidic medium results in the formation of acetic acid and ethanol as given by the equation, For this reaction, the increase in the concentration of acetic acid is determined by measuring the ph of the solution (sample). The concentration values obtained at different time intervals are then plotted on a graph of concentration versus time. The average rate and instantaneous rates of the reaction are subsequently obtained. Factors Influencing Rate of a Reaction Rates of chemical reaction depend on the inherent characteristics or nature of the reactants. That is the reason, why some reactions are fast while others are slow. For example, oxidation of ferrous ion by KMnO 4 (potassium

15 permanganate) in acidic medium is fast, While the oxidation of oxalate ion by the same reagent is slow. Apart from the nature of the reactants, the factors that may affect the rate of a reaction are as follows: Concentration of the reactants: In most cases, the rate of a reaction is accelerated with increase in concentration of a reactant. A piece of wood burns faster in oxygen than in air. Temperature at which the reaction occurs: An rise in temperature increases the rate of a reaction. Cooking at sea level takes less time than on the mountain top because water boils at lower temperature at sea level than at the mountain top. Concentration of catalyst (in homogenous reactions): A catalyst usually speeds up the rate of reaction although it is not consumed in the reaction. Oxidation of sulphur dioxide (SO 2 ) to sulphur trioxide (SO 3 ) is a very slow reaction. However, this reaction accelerates in the presence of nitric oxide (NO). Surface area: In a heterogeneous reaction an increase in surface area of a solid reactant or catalyst leads to an increase in the rate of a

16 reaction. A reaction between a solid phase and a gas or between a solid and a liquid occurs on the surface area of the solid. For example, when charcoal is crushed to powder it ignites easily to produce a flame; solid charcoal has been subdivided into many smaller particles with larger surface area per volume and therefore burns rapidly. Dependence of Rate on Concentration Guldberg and Waage first enunciated the quantitative relationship between the rate of reaction and the concentration of one or more reactants add products, known as the law of mass action. It states that the rate at which a substance reacts is proportional to its molar concentration (moles per litre) and the rate of a chemical reaction is directly proportional to the product of molar concentration of the reactions. The representation of rate of reaction in terms of concentration of the reactants is known as rate law. It is also called the rate equation or rate expression. Rate Expression and Rate Constant Let us consider a reaction of a simple type. In this reaction, only a single substance undergoes the reaction and, thus, the rate of the reaction will depend only on the concentration of A. Mathematically, it may be expressed as: Rate = k [A]

17 Where [A] represents the molar concentration of A while k is a constant of proportionality for this reaction and is known as rate constant. The rate constant is also called velocity constant or specific reaction rate. Similarly, for a reaction between two species A and B, For this reaction, the rate of the reaction can be written in accordance with law of mass action, as: = k [A] [B] Where [A] and [B] represent the molar concentrations of the reactants A and B respectively. If the concentration of each of the reactants involved in the reaction is unity i.e., [A] = [B] =1, then substituting these values in the above expression, we get: Rate of reaction = k x 1 x 1 = k Thus, the rate constant of a reaction at a given temperature may be defined as the rate of the reaction when the molar concentration of each of the reactants is unity. For another hypothetical reaction, The rate of reaction can depend on the concentrations of A and B in the following manners.

18 i) ii) The expressions, k[a][b] and k'[a] 2 [B] are the rate law expressions for the rate of the reaction and k is the rate coefficient or specific rate constant of the reaction. There can be other rate law expression for the same hypothetical reaction given above such as, Rate = k''[a][b] o Rate = k'''[a] 1/2 [B] 1 Theoretically, there are many possibilities to rate law expression of a reaction. However, only one expression will fit the experimentally determined rate data. In general, for any hypothetical reaction, The rate law expression can be written as, Rate (r) = k [A] a [B] b. It is an equation that relates the true rate of reaction to the concentrations of the reactants raised to some power. From the experimental study of the reaction, the dependence of the rate of reaction have been found to be proportional to the concentrations of the reactants raised to some power, Rate = k [A] x [B] y. where x and y are constant numbers or the powers of the concentration of the reactants A and B respectively upon which the reaction depends. The values of x and y are determined experimentally and may or may not be

19 equal to a and b stoichiometric coefficients represented in the reaction. The rate equation, expresses the observed rate of a reaction in terms of the concentrations of the reacting species which influence the rate of the reaction. The rate constant k is independent of concentration but is usually dependent on temperature. Its units depend on the order of the reaction. The rate law is deduced from experiments by studying the concentration dependence of reactants. One cannot evaluate this from stoichiometric coefficients of the equation. This aspect will be clear on examining some of these examples. Example: In the reaction of nitrogen dioxide and fluorine, The rate of the reaction is proportional to the product of the concentration of nitrogen dioxide and fluorine, as observed experimentally. Therefore, the rate of the reaction is expressed as, Rate = k [NO 2 ] [F 2 ]. And not according to the stoichiometry of the chemical reaction. Example: When one starts with 0.01 M concentration of both A and B, the initial rate of the reaction is In second experiment, the initial concentration of A is doubled (from 0.01 M to 0.02 M) keeping concentration of B constant, the rate becomes four times (i.e., changes from to 0.020). This means that the rate of the reaction is proportional to the square of the molar concentration of A, i.e., Data for a hypothetical reaction,

20 Experiment Molar Concentration [A] [B] Rate of Reaction I II III Similarly, when the concentration of B is tripled (from 0.01 to 0.03 M) keeping concentration of A constant, the rate also becomes triple (experiment III from to 0.060). The rate of reaction is, therefore, proportional to the concentration of B, i.e., The rate law equation may be written as Rate = k [A] 2 [B]. For the hydrolysis reaction of ethyl acetate Rate = k [CH 3 COOCH 2 CH 3 ] 1 H 2 O] 0 In all these reactions, the powers of the concentration terms are not same as the stoichiometric coefficients given in the chemical equations. Thus, rate law for any reaction is an experimentally determined quantity and cannot be predicted by merely looking at the balanced chemical equation. Rate law expression serves three purposes. If the composition of the reaction mixture and the rate constant are known, then the rate of the reaction can be predicted.

21 It is useful in postulating the mechanism of a reaction It is useful in classifying the reactions into various orders. Example: Express the relationship between the rate of production of iodine and the rate of disappearance of hydrogen iodide in the following reaction: Solution Rate of production of iodine = 1/2 x Rate of disappearance of HI Example The rate of formation of a dimer in a second order dimerisation reaction is 9.1 x 10-6 mol L -1 s -1 at 0.01 mol L -1 monomer concentrations. Calculate the rate constant. Solution Let the second order dimerisation reaction be, 2A A 2 Rate of formation of dimmer (r) = k [Reactant] 2 = k[a] 2 r = 9.1x10-6 mol L -1 s -1 = k (0.01 mol L -1 ) 2 or,

22 Order of a Reaction The order of a reaction is the power to which the concentration of a reactant is raised. The order of reaction is determined with respect to each reactant in the reaction. For the reaction, Where there are more than one reactants, the order of the reaction is determined with A and then with B. For a general reaction, The reaction rate is described by the expression, Rate= k [A] p [B] q [C] r Where, k is the rate constant of the reaction. [A], [B] and [C] are the molar concentrations of the reactants A, B and C. Then, Order of the reaction with respect to A = p Order of the reaction with respect to B = q Order of the reaction with respect to C = r And, Overall order of the reaction = p + q + r. The sum of the powers of all the concentration terms in the rate law equation is called the order of reaction. The total number of concentration variables which determine the rate of any reaction, is called the overall order of the reaction. Characteristics of Order of Reaction The order of a reaction is generally a small integer, half-integer or zero. It may have any value such as, 1, 2, 3, 1/2, 3/2 or 0.

23 Order of reaction is obtained from the experimentally obtained rate concentration data. So, order of reaction is an experimental parameter. Generally, reaction order cannot be deduced from the stoichiometry of the reaction. Order of the reaction depends on the way a reaction goes through to completion. This could be either in one elementary step or a series of complex steps. If the reaction takes place in a single step then the stoichiometric coefficient(s) of the reactant(s) in the balanced chemical equation gives the order of the reaction with respect to the respective reactant. The overall order then is given by the sum of all the stoichiometric coefficients. In complex reactions the reaction order is to be determined experimentally. Reactions of Different Orders As the sum of the powers of all the concentration terms in the rate law equation is called the order of reaction, reactions can be classified on the basis of the sum of p + q + r., or in terms of the total number of concentration variables which determine the rate of reaction. This is illustrated below. Zero Order Reactions The reaction whose rate does not depend upon the concentration of the

24 reactant is called a zero order reaction. Thus, for a zero order reaction Thus, the rate of a zero order reaction remains constant with time. For example: Reaction of H 2 and Cl 2 over the surface of water is a zero order reaction. Many surface reactions and enzyme reaction under certain conditions are also zero order reactions. First Order Reactions The reaction whose rate depends upon only one concentration variable is called the first order reaction. For a first order reaction involving a reactant A, the reaction rate is given by the equation, Reaction rate = k[a] The reaction rate of a first order reaction varies linearly with the concentration of A (the reactant). Thus, if [A] is halved, the reaction rate also gets halved and if [A] is doubled, the reaction rate also gets doubled. Some typical first order reactions are listed below: Reaction Experimental Rate Law Reaction Order w.r.t. Reactant Overall 2N 2 O 5 4NO 2 + O 2 R t = k[n 2 O 5 ] N 2 O 5 : 1 1 NH 4 NO 2 2H 2 O + N 2 R t = k[nh 4 NO 2 ] NH 4 NO 2 : 1 1

25 2H 2 O 2 2H 2 O + O 2 R t = k[h 2 O 2 ] H 2 O 2 : 1 1 Second Order Reactions The reaction whose rate depends two concentration variables is called a second order reaction. For a second order reaction, involving the reactant A, the reaction rate follows the equation, Reaction rate = k[a] 2 In such a case, the reaction rate varies to the second power of the reactant concentration. For a second order reaction when the concentration of the reactant (A) is doubled, the reaction rate gets increased by a factor of four. A reaction involving two reactants A and B is said to be of second order, if the rate of reaction depends upon the concentration variables of the two species A and B. Some typical second order reactions are listed below. Reaction Experimental Rate Law Reaction Order w.r.t. Reactant Overall H 2(g) + I 2(g) 2HI (g) R t = k[h 2 ] [I 2 ] H 2 : 1, I 2 : 1 2 3NO (g) N 2 O (g) R t = k[no] 2 NO: 2 2 +NO 2(g) Units of Rate Constants for Different Orders Since rate is the change in concentration with time, the rate of a reaction is expressed by concentration units (mol L -1 ) divided by time (s -1 or min -1 ) units. The rate constant (k) of a reaction is not a constant in mathematical terms and its units depends upon, The units in which concentration is measured The unit in which time is measured

26 The order of reaction Units of Rate Constant for Reactions of Different Orders: Reaction Order Rate Law Rate Constant (k) Unit of Rate Constant (k) 0 Rate = -k [A] = k 1 Rate = -k [A] mol L -1 - s -1 mol L -1 min -1 s -1 = time -1 min -1 2 Rate= -k [A] 2 mol L -1 s -1 = concentration -1 time -1 mol -1 L min -1 3 Rate= -k [A] 3 mol -2 L 2 s -1 = concentration -2 time -1 mol -2 L 2 min -1 Example: With the help of the following rate expressions of the reactions, find out the overall order of the reactions and the order with respect to the following reactant: (a) For reaction : (b) For reaction : (c) For reaction : Solution The order with respect to each reactant and the overall order of the reaction are tabulated below:

27 Reaction Rate Order Overall Order (i) k[no] 2 [O 2 ] wrt NO 2 = 2, wrt O 2 = 3 1 (ii) k[n 2 O] wrt N 2 O = 1 1 (iii) k[so 2 Cl 2 ] wrt SO 2 Cl 2 = 1 1 Example: Hydrogen (H 2 ) gas reacts with bromine (Br 2 ) gas to give hydrogen bromide vapour. The chemical reaction is represented by the equation as follows: This reaction determined experimentally follows the rate law, Rate (r) = k[h 2 ] [Br 2 ] 1/2 The reaction is first order with respect to hydrogen and (half order) with respect to bromine. From the above examples, it is clear that various reactions can have various orders. To arrive at a rate law expression for a reaction, it is important to determine the order of the reaction with respect to each of the reactants in the reaction. Molecularity of a Reaction Elementary reactions are classified according to their molecularity. The number of reacting species, which are involved in simultaneous collision to bring about a chemical reaction, is called the molecularity of the reaction. In a unimolecular reaction, a single molecule shakes itself apart or its atoms into a new arrangement. For example, decomposition of NH 4 NO 2 to N 2 and 2H 2 O,

28 Bimolecular reactions involve the collision of a pair of molecules. Bimolecular reactions are common. For example, oxidation of nitric oxide by ozone, Termolecular or trimolecular reactions, three molecules collide simultaneously. Such reactions are rare. The molecularity of a reaction is the number of chemical species i.e. number of molecules, atoms or ions that participate in the reaction, leading to the formation of the products(s). For example: When the reaction takes place through molecular collisions then, the molecularity of the reaction is, the number of atoms, molecules or ions, which must collide together at the same time, leading to the formation of products. Molecularity is applicable for elementary reactions where as, order corresponds to the overall reaction. The overall reaction might involve one elementary reaction or it might be a complex reaction, involving a sequence of elementary reactions. A bimolecular elementary reaction exhibits second order kinetics. This is easy to comprehend. However, if a reaction exhibits second order kinetics, it is not necessary that the reaction involves bimolecular collision. The reaction might involve a sequence of steps, where the molecularity of one step might be different from another step. Hence, knowing the order of a reaction alone, that is the rate law, is not enough to predict the mechanism of a reaction, whereas knowing the reaction

29 mechanism does allow for the deduction of rate law. In reactions, which involve a single elementary reaction the rate law can be written from the stoichiometry of the chemical equation. One such reaction is the gas phase reaction of ozone (O 3 ) with nitric oxide (NO). This bimolecular reaction exhibits second order kinetics. However, overwhelming majority of reactions consists of several connected elementary reactions, that is, they are complex reactions. A sequence of elementary reactions leading to the overall stoichiometry of the reaction is called mechanism of the reaction. The mechanism of a reaction is postulated based on experimental observations such as, temperature dependences of reaction rates, concentration dependences of reaction rates, effect of catalysts etc. Radioactive tracers sometimes yield valuable information about the mechanisms. Spectroscopic identification of short-lived intermediates helps in postulating the most appropriate mechanism. The concentration-dependence of reaction rate provides first hand information regarding the mechanism of reactions. Then, the rate law is predicted from the mechanism. If the deduction of rate law rate law matches the experimental rate law, then the hypothesized mechanism can be accepted as the most probable mechanism of reaction. Elucidation of reaction mechanism is more like detective work where the 'happening' of an 'event' is constructed based on a series of clues. In reaction mechanism studies, identification of intermediates forms an important area of study. Study of complex reactions is based on certain methods that have been developed over the years. Complex reactions can involve a series of consecutive reactions (series reactions), they can also react via parallel reactions giving rise to multiple products.

30 Characteristics of Molecularity The molecularity of any process can only be a small positive integer and cannot be zero, fractional or negative. Molecularity of a reaction depends upon the mechanism postulated for the reaction and is not an experimental parameter. The molecularity of a reaction is not the same as the order of reaction. However, for an isolated, single step reaction, the molecularity and the order of the reaction are equal to each other. When a reaction proceeds through two or more elementary reactions, each elementary reaction has its own rate. Some elementary reactions may be fast, while others may be slow, the rate of formation of a product cannot be faster than the rate of the slowest elementary reaction. The slowest elementary reaction in any mechanism is called the ratedetermining reaction or rate determining step. The rate of the overall reaction, i.e., the rate of formation of the final products, is governed by the rate of the slowest elementary reaction. For example, in a reaction, The overall rate of reaction is governed by the rate of the slowest step, as its half-life is the longest (1s) in this sequence of reactions. The rate of formation of G and H will be governed by the slowest step.

31 The concept of the rate-determining step can be likened to the flow of water through pipes of different sizes. It is obvious, that the overall flow of water cannot be faster than the rate of flow of water through the narrowest pipe. The low rate through this narrow tube will decide the rate at which water flows out of the last tube, i.e., the rate at which water is drawn out from the outlet. The usefulness of the rate-determining step in writing the rate equations is illustrated below. In the reaction, Proceeds through the following two elementary reactions The step I being a slow step is the rate-determining. Therefore, the rate of reaction is governed by step 1. Thus, Reaction rate = k [NO 2 ] [F 2 ]. This rate law is the same that is observed experimentally. Thus, the reaction has order 1 with respect to NO 2 and 1 with respect to F 2, and the overall order of the reaction is 2. Molecularity differs from order of a reaction. The differences are listed below: Molecularity It is the number of reacting species Order It is the sum of the powers of the concentration terms in the rate law undergoing simultaneous expression. collision. It is a theoretical It is experimentally determined.

32 concept. It has integral values It can have fractional values also. only. It cannot be zero. It provides no information on reaction mechanism. It can be zero. The slowest step in the reaction can be judged by the order of the reaction and this gives further information about the mechanism. Integrated Rate Equations The rate equations that have been discussed so far giving the concentration dependence are in their differential form as shown. This equation is a differential equation that relates the rate of change in a concentration to concentration itself. It is also a measure of the instantaneous rate as measured by the slope of the tangent drawn to an instant point (t) in the concentration versus time plotted graph. This makes it difficult to determine the rate law and hence the order of the reaction. Since such differential rate equations do not give an accurate picture of the entire range of the reaction proceeding in a given time, the differential equations are integrated over the meaningful range of the experimental data within the time period. The integral forms of the rate law expressions are called integrated rate equations. These equations give a relation between directly measured concentrations of reactants or products with time, and the rate constant.

33 The integrated rate equations are different for the reactions of different reaction orders. Zero Order Reactions As explained before, when a reaction has a rate which is independent of the concentration of the reactant(s) it is called a zero-order reaction. In the above reaction increasing the concentration of the reacting species A will not speed up the rate of the reaction. d[a] = k dt If this differential equation is integrated both sides [A] = - kt + I Where, I is the integration constant. At t = 0, the concentration of the reactant A = [A] 0, where [A] 0 is initial concentration of the reactant. Substituting in above equation [A] 0 = -k x 0 + I [A] 0 = I Substituting the value of I, gives an equation which is often called the integrated zero-order rate law.

34 [A] = - kt + [A] 0 Where [A] represents the concentration of the chemical of interest at a particular time and [A] 0 represents the initial concentration. Zero order rate constant is given as, The reaction is zero-order if it occurs in a closed system when there is no net build-up of intermediates and there are no other reactions occurring. For a zero order reaction the concentration versus time profile is linear and the rate of reaction versus time has the profile as shown in the graph. The slope of this resulting line is the zero order rate constant - k and intercept [A] 0.

35 Zero-order reactions occur rarely under speacial conditions only. Reactions in heterogenous system usually follow zero order kinetics. They are typically found when a material required for the reaction to proceed, such as a surface or a catalyst. In such a system the reactants are adsorbed on the surface of a solid catalyst. At low concentrations of the reactant, the rate of the reaction depends on the fraction of the surface covered by the reactant. However, at higher concentrations the surface of the catalyst becomes fully covered and any further increase in the concentration of the reactants does not affect the rate of the reaction. One very common example is the decomposition of ammonia (NH 3 ) on finely divided platinum. Example Ammonia (NH 3 ) gas decomposes over platinum catalyst to give nitrogen gas (N 2 ) and hydrogen gas (H 2 ). The chemical reaction is as follows: The reaction follows zero order kinetics. Therefore the rate law is rate r = k[nh 3 ] o

36 In this reaction, the platinum metal surface gets saturated with gas molecules at high pressure. So, a further change in reaction conditions is does not alter the amount of ammonia on the surface of the catalyst making rate of the reaction independent of its concentration. First Order Reactions For a first order reaction with rate constant (k), at time (t) the initial concentration [A] 0 will change to the new concentration at time t [A] t. The rate of formation of X from the chemical reaction: Where the initial concentration of A is [A] o. And the initial concentration of X is 0. The concentration of X at time t is [X] t. The concentration of A at time t is [A] t. The rate of a reaction is: The rate for a first order reaction is: Rate = k[a] t These two may be combined as: The concentration of A at time t may also be written in terms of X (the amount that has reacted) since the area under a plot of [A] vs time is the amount that has reacted.

37 The above figure is an example of the first order reaction. The rate of the reaction depends on the concentration of the reactant. Initially the rate is fast and then it slows down as the concentration of the reactant falls. Radioactive decay of unstable nuclei takes place by first order reaction. Example: Cyclopropane (C 3 H 6 ) at room temperature has a ring structure. When it is heated, the ring opens up and cyclopropane isomerizes to propylene. The reaction takes place in a first order manner. Therefore, the rate law for the reaction is, rate (r) = k [C 3 H 6 ] 1 In terms of X the concentration of A at time t in the rate law equation is given as:

38 The above equation may be rewritten as: This equation rearranges to: Integrating this function with very small changes in X and t, we have, - ln ([A] o - [X]) = kt +C C is the integration constant, which can be evaluated as, At t = 0, X = 0 so that - ln ([A] o - 0) = k0 +C C = - ln [A] o Substituting this expression into the above so that: - ln ([A] o - [X]) = kt + - ln [A] o This rearranges to give: ln [A] o - ln ([A] o - [X]) = kt Since [A] o - [X] at time t is also [A] t, this may be rewritten as follows:

39 This is the integrated first order rate equation, which rearranges in different ways for different applications: When the concentration of the reactant are [A] 1 and [A] 2 at time t 1 and t 2 respectively then the above equation can be written as, Taking antilog on both sides, the equation arranges to, In the log form the first order rate equation is written as, A plot of ln [A] t against t gives a straight line with slope = -k and intercept equal to ln [A] 0.

40 If a graph is plotted between log [A] 0 /[A] t vs t, the slope = k/2.303 Example: Decomposition rates of N 2 O 5 g at different values of concentrations of N 2 O 5 as given in the data below: N 2 O 5 x 10-2 M Rate Ms These values are plotted as rate versus concentration in figure below.

41 It is seen that the rate is proportional to the concentration of N 2 O 5 raised to the power one. Therefore, dinitrogen pentoxide decomposes in a first order manner. The value of the rate constant k, as evaluated from the data, is k = 3.0 x 10-2 min -1 In a gas phase reaction, The concentration term is replaced by the pressure to give the following equation. Where p i is the initial pressure and p t is the total pressure of the system. In terms of partial pressure p A of A the equation is, Example: From the following data show that the decomposition of hydrogen peroxide is

42 a first order reaction. Time in Minutes Volume of KMnO 4 (ml) Solution: If the reaction is first order, it should follow the equation, In this case the initial volume V 0 i.e., volume at t = 0 corresponds to the initial concentration i.e., [A] 0 and the volume at time t V t corresponds to the concentration at that time [A] t. Substituting these values in the above equation, The value of k at 10 min is, At 20 min k is, Since the value of k is nearly the same the reaction is first order. Half Life of a Reaction The time taken by a reaction to proceed to a definite stage say 98% completion is the life-time of a reaction. The shorter the life-time the faster is the reaction. However, most of the time a reaction goes very slowly when near completion. The determination of the life time of the reaction is usually not possible for all practical considerations. Hence, the term half-time or half-life period is formulated to define the time period of a reaction.

43 The half-time (or half-life period) of a reaction may be defined as the time period during which the concentration of a reactant gets reduced to one-half (50%) of its initial value or the time required for the completion of 50% of the reaction. Half-life time is denoted by t 1/2 and its value depends upon the speed of the reaction. Fast reactions have short half-life time, while slow reactions have long half-life time. For a zero-order reaction the rate constant is Substituting this in the above equation we have, Half-life is given as, It is clear that t 1/2 is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant for a zero order reaction. The half life (t 1/2 ) of the first order reaction can be derived from the rate constant as follows:

44 When the reaction has proceeded half way then [A]=[A] o /2. On substitution of this value in the integrated equation the expression of t 1/2 becomes, or The effect of initial concentration of the reactant on the half time of a reaction depends upon the order of the reaction. This is illustrated below. Order of Reaction 0 Half Life Time (t 1/2 ) Concentration Dependence of t 1/2 t 1/2 Initial conc. of reactant 1 t 1/2 Independent of initial conc. of reactant Only for the first order reaction t 1/2 is independent of the initial concentration of the reactant. This relation can be used to determine the order of a reaction. In general, for a reaction of order n, t 1/2 is proportional to initial concentration of A raised to power n - 1, that is,

45 Example: A first order reaction has k=3 x 10-6 s -1 at 513 K. The reaction is allowed to run for five hours. After this time interval what percentage of the initial concentration would have changed into products? What is the half-life of the reaction? Solution: In the integrated rate law expression k is given as On substitution, the expression becomes

46 = Hence, 5.2% of the initial concentration has changed to products. Example: A first order reaction is 40% complete in 50 minutes. What is the rate constant? In what time will the reaction be 80% complete? Solution: It is given that the reaction is 40% complete in 50 min Hence, [A] t = [A] o - 0.4[A] o = 0.6[A] o The advantages of the integrated form of the rate law are: It gives the concentrations for all times. It is helpful in determining the time in which the reaction is 10% or

47 60% or 99% complete. The variation of concentration with time is better understood by using the integrated form of the rate law. Half - life expressions, obtained from the integrated form are used in the determination of order of a reaction. The rates of chemical reactions vary from the fastest with reaction times of the order of seconds to the slowest with reaction times of the order of millions of years. Modern techniques, mainly using lasers, are now available to study extremely fast reactions. Reaction Reaction Times (Half Life) First step of photosynthesis: S First step in vision: Retenial isomerisation Sucrose + Water Glucose + Fructose 200 min 60s 1000 h 2000 year Pseudo First Order Reaction In some acid catalyzed reactions like the inversion of cane sugar and hydrolysis of ethyl acetate, the stoichiometric equations show them to be bimolecular but they are found to be first order by experiment.

48 For the inversion of cane sugar reaction the rate of reaction is proportional to the concentration of sucrose only. So, in the rate equation, Rate = k' [C 12 H 22 O 11 ] [H 2 O] The term [H 2 O] is constant. The equation, thus, becomes Rate = k [C 12 H 22 O 11 ] Where k = k' [H 2 O] As the reaction behaves as first order reaction, such reactions are called pseudo first order reactions. Similarly in the hydrolysis of ethyl acetate, the rate of reaction is proportional to the concentration of ethyl acetate only. The reason for such behaviour arises from the fact that water is present in such a large extent that its concentration remains almost constant during the course of the reaction. The rate law for the reaction is expressed as rate = k [A] m [B] n If the concentration of B is kept large, then [B] essentially does not change over time and if the rate of reaction is determined as rate = k [A] (m = 1) then this reaction is a pseudo first order reaction. Acidic hydrolysis of ethyl acetate and conversion of cane sugar are examples of a pseudo first order reaction, where the hydrolysis is carried out in excess in the solvent, acidic water.

49 Temperature Dependence of the Rate of a Reaction The reaction rates of most chemical reactions are significantly influenced by change in temperature. An alteration of temperature conditions in which a reaction takes place, increases or decreases the rate of almost all reactions. A general approximate rule for the effect of temperature rates on reaction rates is, for every 10 C rise in temperature the rate of reaction almost becomes double. The temperature coefficient of a reaction, defined as a ratio of the rate constants at two temperatures of a particular reaction differing by 10 C (usually measured from 25 C to 35 C), gives the dependence of reaction rates on temperature It is given by, Temperature coefficients for most of the reactions lie between 2 and 3, i.e., the rate constant can double (or even triple) when the temperature is raised by ten degrees near the normal room temperature. The effect of temperature on the rate constant is mathematically expressed by the Arrhenius equation. Arrhenius studied gas phase reactions and in 1897 arrived at an empirical equation that described the temperature dependence of reaction rate constant 'k' by the equation, The equation called Arrhenius equation indicates exponential dependency of the rate constant on temperature. Here 'A' is the Arrhenius factor or the frequency factor also called the pre exponential factor. It is a constant specific to a particular reaction. E a is the energy of activation for the reaction measured in joules/mole (Jmol -1 ), R is the gas constant, T the temperature, and the exponential factor (-E a /R T ) is a measure of the probability for the occurrence of a molecule at the top of the energy-barrier.

50 Activation Energy and the Rate of Reaction According to Arrhenius the conversion of the reactants into products does not take place of its own like 'a down the slope process', instead the reacting molecules must cross an energy-barrier before they get converted to products. The energy-barrier is an imaginary high-energy state between the reactants and products. Once molecules cross the top of this barrier they will be able to react. Before a reaction commences, reacting molecules are at their normal level or their average potential energy at room temperature. This energy is less than the energy called the 'Threshold energy' which is the required to interact and cross the energy barrier. In order for reacting molecules to break old bonds to form new ones, sufficient energy is needed to cross the threshold. This minimum energy over and above their average potential energy must be acquired by the reacting molecules in order to cross the energybarrier and be able to start reacting and change into products. The energy required for crossing the energy barrier comes from the kinetic energy of reacting molecules. The additional energy which the reacting molecules must acquire over their average potential energy, to be able to start reacting, is called the activation energy of the reaction (E a ). It is quite obvious that the reactant molecules will not be able to react unless energy equal to the activation energy is given to them. E a = E T - E R Where, E a is the activation energy of the reaction; E T is the threshold energy; E R is the average energy of the reactant molecules. Each reaction also has a typical energy of activation value E a. The concept of activation can be easily visualized from the below figure.

51 So, it is seen that, When the activation energy is small, then larger number of the reactant molecules will be able to cross over the top of the energy-barrier, and the reaction will be faster. Thus, if the activation energy is low, then the reaction is fast. When the activation energy is high, then only a few molecules would be able to cross the top of the energy barrier, and the reaction will be slow. Thus, if the activation energy of a reaction is high, then the reaction is slow. When the activation energy is zero, then each molecule will be able to cross the top of the energy barrier, and the reaction will be instantaneous, and almost explosive. Thus, if the activation energy of a reaction is zero, then the reaction is instantaneous and very, fast. This can be easily determined from the Arrhenius equation. The exponential value is larger for a low E a as compared to the value of the exponential with high E a. In other words, if low E a is E a1 and high E a is E a2, then k 1 greater than k 2 where the indices 1 and 2

52 represent reaction 1 and reaction 2 of a specific reaction type respectively. Transition State or Activated Complex Theory According to Arrhenius, the reactants do not get transformed into products directly. The reactant molecules first form a high-energy configuration (of an arrangement of atoms), corresponding to the top of the energy-barrier. The high-energy configuration is an unstable intermediate or 'transition state' which exists for a very short time and then decomposes to form the products. This state is called 'activated complex'. A simple way of visualizing the concept of the transition state is to think of a reaction proceeding along a reaction coordinate. For example, in a reaction two reactants A and B react to form the activated complex leading to product formation. As long as 'A' and 'B', are away from each other, their total energy is nearly constant. When 'A' approaches 'B', along the inter-nuclear axis (B B bond) and comes closer to it, 'A' starts pulling one of the 'B' atoms (in B 2 ). This results in stretching of B B bond and therefore an increase in the energy of the system. At some suitable distance between 'A' and 'B' a configuration A... B... B is formed in, which both the distances A B and B B are greater than the equilibrium bond lengths. Therefore the configuration A... B... B possesses higher energy than the combined energies of 'A' and BB2, and corresponds to the top of the energy barrier. As 'A' comes closer to 'B', a bond is formed between 'A' and 'B' i.e., A B is formed. As the complex decomposes to form the products, some energy is released and consequently, the energy of 'AB' and 'B' is less than that of 'A' and 'B'. During the reaction, the A B and B B separation change continuously. So, the change in inter-nuclear separation is termed as the reaction coordinates. One can understand the above concept clearly by looking at the formation of activated

53 complex (or transition state) in the reaction between H 2(g) and I 2(g). It can be represented as: One can see that as H and I come close, the energy of the system goes up and reaches a maxima. The arrangement of the atoms or molecules corresponding to this energy maximum is the transition state. Therefore, the energy level of the transition state is higher than that of the reactants. The energy of the system goes down i.e., energy is released as soon as the transition state breaks and decomposes to transform into products. The transition state is considered to be a stable molecule except for the motion of the

54 atoms along the reaction coordinate. Transition state is supposed to be in equilibrium with the reactants. It also has a very short life. That is why, when it was proposed in the 1930s, it was not possible to study the transition state with the techniques available then. With the help of laser pulses of 'femtosecond' to 'picoseconds' lengths, transition state has been shown to exist. It was only recently, in 1988, that existence of the transition state has been proven and characterized spectroscopically in a gas-phase reaction by Zewail and Bernstein. Arrhenius explained the dependence of reaction rates on temperature by saying that in the formation of products, molecules must have energy equal to or more than the 'threshold energy'. He further based this fact on the distribution of energy amongst the molecules of the reacting system.

55 At any temperature, the number of molecules possessing energies equal to or greater than a certain energy (say, 'E') is proportional to the area under the curve beyond that energy (the shaded area shown in the Figure (a). When the temperature is increased, the distribution gets broadened and the area under them curve beyond 'E' increases, shown in Figure (b). Thus, at higher temperature, more molecules would possess energies equal to or greater than certain energy i.e., threshold energy. Therefore with a rise in temperature, more molecules are able to take part in chemical reaction. As a result, the reaction rate increases with an increase in temperature. According to Arrhenius, a rise in temperature, increases in the rate of reaction mainly due to the increase in the number of molecules possessing energies equal to or greater than the threshold energy for the reaction. Determination of Activation Energy Activation energy of a reaction can be determined by graphical or numerical analysis of Arrhenius equation. Graphical Method Arrhenius equation for the rate constant of a reaction is Where, E a is the activation energy of the reaction. Rewriting Arrhenius equation by taking logarithm on both the sides, one can write,

56 Thus, a plot of log k against 1/T should be a straight line as seen in the figure above. The slope of this straight line is given by Slope = -E a /2.303 R So, E a = x R x (-Slope) Thus, one can write, Activation energy E a = x R x (-Slope) Where, R is the universal gas constant: R = 8.314J K -1 mol -1 Numerical Method When the rate constant values at only two different temperatures of a reaction are known, this method is generally used. If only two values of the rate constant at two different temperatures (T 1 and T 2 ) are known, then one can write

57 Subtracting one equation from the other, one gets Thus, knowing k 1, k 2 and T 1, T 2, E a can be obtained from the above equation. Example The rate constants of reaction at 700 K and 760 K are M -1 s -1 and M -1 s -1 respectively. What are the values of 'A' and 'E a '? Solution Arrhenius equation is T 1 = 700 K, T 2 = 760 K, k 1 = M -1 s -1, k 2 = M -1 s -1 Substitution of these values in the equation gives

58 E a = KJ / mol ln A = A = 2.8 x s -1 Example What is the activation energy of a reaction whose rate quadruples when the temperature is raised from 293 K to 313 K. Solution or, E a = KJ / mol Example For a reaction with activation energy of 55 KJ/mol, by what factor will the rate constant

59 go up with a rise in temperature from 300 K to 310 K. Solution Where k 2 is the rate constant at 310 k and k 1 is the rate constant at 300 k. This example shows that for a 10 degree rise in temperature, close to the room temperature, results in doubling of the rate of the reaction. Kinetic Rates and Thermodynamic Properties Transition state theory attempts to relate the kinetic rates with thermodynamic properties of the transition state and reactants. Any elementary reaction, The transition state is in equilibrium with the reactants. Therefore, the equilibrium constant K * can be given as, Now, the formation of the product P is given by,

60 Once the transition state is formed, then the products are formed with a frequency equal to k B B T/h. That is, where, K * = k B B T/h, k B B is the Boltzmann's constant and h is the Planck's constant. On substitution of this expression in equation the expression for k becomes, Now, from thermodynamics, it is known that the equilibrium constant K is related to the free energy of the reaction. Hence, G * for the formation of the transition state, which is also the free energy of activation is given by, Then the equation for k transforms to, The same derivation should hold for the reverse reaction. This implies that the free energy of the reaction is The change in free energy of the system along the reaction coordinate is shown in the figure below.

61 At constant temperature, G * is related to the enthalpy of activation H * and to the enthalpy of activation S * as follows: Enthalpy of activation and entropy of activation are incorporated into the rate constant equation as follows: The equation shows that the rate constant of a reaction is affected by entropy and enthalpy. Transition state theory predicts slightly different temperature dependence from that of Arrhenius. However, both predict exponential temperature dependence for the rate constant k. Entropy of activation ΔS * is related to the change in the configuration of the reactant species along the reaction path. With the formation of transition state, there is a loss in the randomness, and therefore the entropy of activation is usually negative. Activation Energies of a Reversible Reaction

62 In a reversible reaction, the reactants react to form products, and the products react back to give the reactant molecules. Thus, in a reversible reaction, there are two reactions proceeding in the opposite directions. Each reaction has its own characteristic activation energy. So, in a reversible reaction there are two activation energies: one for the forward reaction, and the other for the backward reaction. These are commonly called as the energy of activation for the forward reaction (E a, f ) and the energy of activation for the backward reaction (E a, b ) When the energy of the products is lower than that of reactant, then activation energy for the forward reaction < Energy of activation for the backward reaction. Or, E a, f < E a, b Therefore, the reaction in the forward direction is faster than that in the backward direction. When the energy of products is higher than that of the reactants then activation energy for the forward reaction > Activation energy for the backward reaction or Thus, the reaction in the forward direction is slower than the reaction in the backward direction. The activation energy of a reaction in any direction determines the speed (rate) of reaction in that direction. It does not say anything about the extent of reaction in that direction. Extent of reaction in any direction is governed by the equilibrium constant of the reaction. In a reaction, the energy change is given by: Energy change in a reaction = Energy of products - Energy of reactants or

63 According to the concept of activation energy, the reactant molecules in the forward reaction and the products molecules in the backward reaction must pass over the top of the energy-barrier (E T ). Then, one can write the above equation in the following form, or Under constant pressure conditions, ΔE = ΔH So, (a) When E a, f < E a, b ΔE = -ve and, ΔH = - ve Thus, when the activation energy for the forward reaction is less than that for the backward reaction, energy is released during the course of reaction. (b) When E a,f > E a,b ΔE = +ve and, ΔH = + ve

64 Thus, when the activation energy for the forward reaction is more than that for the backward reaction, energy is absorbed during the course of reaction. Significance of Activation Energy The existence of energy-barrier between reactant and products in all reactions has an important implication for the existence of life. For example, the reaction between hydrogen and oxygen to form water is thermodynamically feasible ( ΔG = kj mol -1 ). But, a mixture of hydrogen and oxygen can be kept without any reaction for any indefinite period. This mixture however would react to form water when an electric spark is passed through it using platinum electrodes. Also, if there has been no energy-barrier between the liquid water and water vapours, the whole water on the earth would have

65 evaporated almost instantaneously. Similarly, the burning of all common fuels in the presence of oxygen in air is a spontaneous process (ΔG < 0), but fuels do not react with oxygen in the air under room temperature conditions. At room temperature, common fuels like kerosene and liquid petroleum gas are highly stable because of very high energy of activation of the combustion reactions. A mixture of any fuel and air does not burn unless ignited with a spark from a lighter /match stick; this raises the temperature of a small portion of the fuel and thus provides the necessary activation energy for a combustion reaction. Combustion being an exothermic process produces heat and provides activation energy till all the fuel molecules undergo combustion. Effect of Catalyst In certain chemical reactions it is necessary for the reaction to proceed along some other way to complete it, as an increase in temperature above certain limits causes the reactants to become unstable and decompose. This occurs with the help of a catalyst. A catalyst is a substance that changes the reaction rate without undergoing any permanent change after the reaction, in mass and composition of its chemical behaviour. A positive catalyst provides an alternative path to accelerate a chemical reaction by lowering the activation energy for the reaction. It lowers the activation energy for both forward and backward reactions.

66 For example nitric oxide is used to increase the rate of reaction of combination between sulphur dioxide and oxygen to give sulphur trioxide. This is illustrated in figure.

67 The lowering of activation energy by a catalyst permits more and more molecules to take part in the chemical reaction, because more molecules will have energy equal or greater than the lowered threshold energy leading to an increase in the rate of reaction. The action of a catalyst can be explained in terms of the transition state theory. A catalyst is not consumed in the reaction; it is used up in one step and then released in the next step. The catalyst will participate in the reaction by forming temporary bonds on its surface with the reactants, resulting in an intermediate complex. This has a temporary existence and decomposes to yield products and the catalyst. A catalyst does not change the extent of completion of a reaction. It simply speeds up the attainment of the equilibrium i.e., a catalyst does not affect the position of equilibrium in a reversible reaction. Two types of catalytic reactions are usually distinguished according to the number of phases of a system. Homogenous catalysis and Heterogenous catalysis

68 Homogenous catalysts are of the same phase of the reactants. Oxidation of sulphur dioxide (SO 2 ) to sulphur trioxide (SO 3 ) in the presence of nitric oxide (NO) is an example of homogenous catalytic reaction. In heterogenous reaction, the catalyst exists in a different phase from the reactants. Usually a solid catalyst is used and the reactants can be either in the liquid or gaseous phase. Nitric oxide can be replaced by platinum in the above reaction to demonstrate heterogenous catalysis. Here, the surface area of the catalyst affects the rate of the reaction, especially under low reactant concentrations. Another example of heterogenous catalytic reaction is hydrogenation of unsaturated hydrocarbon. Autocatalysis The phenomenon where the reaction rate increases as a product is formed is called autocatalysis. An example of autocatalytic reaction is the Belousov-Zhabotinskii (BZ) reaction. The product HBrO 2 is the reactant in step I. Another example of autocatalysis is the reaction of potassium permanganate with oxalate ion in acidic medium. The reaction is very slow, but once, a crystal of MnSO 4 is added the reaction is accelerated. In this reaction Mn 2+ is formed as a product, which acts as a catalyst. From industrial production point of view, autocatalytic reactions play an

69 important role. The rate of reaction can be maximized by making sure that the optimum concentrations of reactants and products are always present. Collision Theory of Chemical Reactions The collision theory was developed by Max Trautz and William Lewis in and provides a wider insight into the energetic and mechanistic aspects of reactions. It is based on kinetic theory of gases. According to kinetic considerations, a chemical reaction takes place due to the collisions of the molecules of the reacting substances. Consider a homogeneous gas phase reaction in which 'A' and 'B' react to form AB viz, In the first case; Let unit volume contain one molecule each of 'A' and 'B'. Then, number of collisions at any instant = 1 x 1 = 1 In the second case; Let the number of molecules of 'A' and 'B' be two each. Then, number of collision at any instant = 2 x 2 = 4 In the third case; Let the number of molecules of 'A' and 'B' be two and three respectively; then, number of collisions at any instant = 2 x 3 = 6 In general, therefore the total number of collisions per second is given by the product of the number of molecules per unit volume of all the reactants. This is known as collision frequency 'Z' As the number of molecules per unit volume is proportional to the corresponding molar concentration, therefore, for any reaction,

70 Reaction rate (Molar concentration of A) x (Molar concentration of B) [A] [B] or Reaction rate = k [A] [B] Similarly, for the reaction Reaction rate = k [A] [B] [C] And for the reaction, or Reaction rate [A] [A] [B] [A] 2 [B] Reaction rate = k [A] 2 [B] In general therefore, for a reaction n A + m B Products Reaction rate = k [A] n [B] m In the collision theory, only that fraction of total collisions are considered 'effective' (in producing the product), where the molecules posses sufficient energy as well as proper orientation to overcome the energy and orientation

71 barriers, at a given temperature. Let us look more closely at the energy barrier and orientation barriers to reactions in the collision theory. Energy Barrier In this collision theory, the rate constant is related to three factors Z, f and p by the equation k = Zfp Where, Z is the collision frequency f is the fraction of collisions having energy greater than the threshold energy p is the fraction of the collisions that occurs with the reactant molecules properly oriented. Z, the collision frequency increases with temperature because Z is directly proportional to the root mean square (rms) of velocity as given by, Where, σ is the molecular diameter N/V is the number of molecules per cc. From kinetic theory of gases, it is known that V rms has a square-root dependency on temperature, that is,. Therefore, for a given molecular diameter, the collision frequency will also have a square-root dependency on temperature. The ratio of Z values at two temperature values, for e.g., at 298 K and 308 K will be,

72 A ten-degree rise in temperature near the room temperature usually doubles the rate of a reaction, but the factor Z does not change much with temperature and therefore, does not explain doubling of rate of reaction. The reason could be that all collisions do not lead to the formation of products, especially for complex molecules. The factor that contributes to the acceleration of a rate of a reaction is (f), the fraction of collisions having energy greater than the threshold energy. Again, from the kinetic theory of gases it is seen that 'f 'has an exponential dependence with temperature. The effect of this factor on k can be best explained with an example. The reaction of nitric oxide (NO) with chlorine (Cl 2 ) is believed to occur in a single step. The activation energy for the reaction is 8.5 x 10 4 J / mol. At 298 K the fraction of collisions with the energy of activation is 1.2 x This is an extremely small value. However, the frequency of collision Z is very large; therefore, the product of Z and f is not small. For a 10 degree rise in temperature the fraction of collisions with energy greater than the threshold increases to 3.8 x 10-15, this increase is threefold. Therefore, the rate of the reaction or the rate constant increases threefold. The effect of temperature on f can be explained from the energy distribution among molecules at different temperatures. From the energy curves shown below,

73 It is observed that the energy distribution curve is flatter at higher T and is shifted toward higher energy region. This is because, the kinetic energy of the molecules are higher at higher temperatures. Also, the fraction of molecules with energy greater than the threshold as indicated by the shaded portion is almost double. It is very clear, that the rate of reaction increases with temperature, mainly due to increase in the number of collisions which occur with sufficient energy, i.e., with energy greater than the threshold. Orientation Barrier As noted earlier, the rate of reaction also depends on p, the fraction of collisions that occur with proper orientation. This factor is independent of temperature. The importance of proper orientation of the reactant molecule can be understood from the figure.