Lecture 8, Kinetics 22/04/2018. Chemical kinetics studies: Rate. Kinetics, rate of the reaction, reaction mechanism. rates of chemical reactions

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1 /04/08 Chemical kinetics studies: rates of chemical reactions the factors that affect rate reactions Lecture 8, Kinetics the mechanisms (the series of steps) by which reactions occur Rate We are all familiar with processes in which some quantity changes with time Car travels at 40 km/hour (miles/hour) Faucet delivers water at 30 l/min (gallons/minute) Factory produces 3,000 tires/day Each of these ratios is called a rate Kinetics, rate of the reaction, reaction mechanism The speed with which the reactants disappear and the products form is called the rate of the reaction. A study of the rate of reaction can give detailed information about how reactants change into products. The series of individual steps that add up to the overall observed reaction is called the reaction mechanism. 3 4

2 /04/08 When blue dye is reacting with bleach, the latter converts dye into a colourless products. The colour decreases and eventually disappears. The rate of the reaction could be determined by repeatedly measuring both the colour intensity and the elapsed time. The concentration of the dye could be calculated from the intensity of the blue colour. 5 A spectroscopic method for determining reaction rates. Light of the wavelength that is absorbed by the investigated substance is passed through a reaction chamber. The changes in the reactant or product concentration as reaction progresses cause the decrease or increase of the light intensity. 6 Quiz Identify which of the following are rates: A) 5 cm B) 30 m / s C) 5 o C D) 5 o C/min E). mol /min F) 45 min Experience tells us that different chemical reactions occur at very different rates, e.g.. Some reactions proceed very rapidly, even explosively i.e. combustion reactions burning methane (component of natural gas) or isooctane (C 8 H 8 ) in gasoline.. Other reactions carry on very slowly i.e. an erosion of the rocks or an iron rusting 7 8

3 /04/08 We have learnt on the spontaneity of reaction from thermodynamics. But it is hard to state whether all spontaneous reactions are rapid ones. The reactions of strong acids with strong bases are thermodynamically favoured (spontaneous) and occur at very rapid rates. ) HCl + Mg(OH) MgCl + H O ΔG 0 rxn = kj/mol Similarly reaction some compound with oxygen (e.g. burning) is thermodynamically favoured and rapid e.g. ) CH 4 + O CO + H O ΔG 0 rxn = kj/mol But 3) C (diamond) + O (g) CO (g) ΔG 0 rxn = -397 kj/mol This reaction does not occur at an observable rate. 4) C (graphite) + O (g) CO (g) ΔG 0 rxn = -394 kj/mol. This reaction occurs rapidly. The difference in the reaction speed of 3 and 4 reactions is explained by kinetics, not thermodynamics. 9 0 Rate of reaction, v, The rate of reaction describes how fast reactants are used up and products are formed. Knowledge of the rate of a reaction can be an invaluable tool in helping us to understand how chemical compounds behave when they interact. Rate, formula A rate, is always expressed as a ratio. One way to describe a reaction rate is to select one component of the reaction and describe the change in its concentration per unit of time: 3

4 /04/08 (conc.of X at time t conc.of X at time t) rate with respect to X ( t t ) (conc.of X ) t Molarity (mol/l) is normally the concentration unit and the second (s) is the most often used unit of time. Typically, the reaction rate has the units mol/l s or mol L - s - Quiz An 8.00 g piece of magnesium was placed into 6.0 M HCl. After 5 s g of unreacted magnesium remained. The average rate at which magnesium was consumed is: A. 0.4 g/s B. 0.8 g/s C. 0.3 g/s D g/s 3 4 Consider the following reaction at a constant temperature in closed system: MgCO 3(s) + HCl (aq) CO (g) + H O (l) + MgCl (aq) Which of the following properties could be used to determine reaction rate? A. Mass of the system B. Pressure of the gas C. Concentration of H O D. Concentration of MgCO 3 E. Disappearing of solid Consider the following reaction: CaCrO 4(s) +H + (aq) Ca + (aq) + H O (l) + Cr O - 7 (aq) (orange) The progress of the reaction could be followed by observing the rate of A. mass loss B. decrease in ph C. precipitate formation D. formation of orange colour in the solution 5 6 4

5 /04/08 a A + b B c C+ d D rate= -Δ[A]/ Δt; rate = -Δ[B]/ Δt, or rate = Δ[C]/ Δt; rate= Δ[D]/ Δt The reaction rate must be positive because it describes the forward reaction, which consumes A and B. The concentration of reactants A and B decrease in time interval Δt. Δ[A]/ Δt and Δ[B]/ Δt are negative quantities. If no other reaction takes place, the changes in concentration are related to one another. For every a mol/l that described decrease of [A], [B] must decrease by b mol/l, [C] must increase by c mol/l and so on The number of moles of reactants or products that occur per litter in a given time describe the rate of reaction. 7 8 a A+ b B c C+ d D 9 0 5

6 /04/08 Quiz A + B 3C +D If the rate of disappearance of A is equal to mol/l s at the start of the reaction what are the rates of change for B, C and D at this time? Rate of change of B = Rate of change of C = Rate of change of D = a) B= 0.04 M/s; C= M/s; D= mol/l s b) B = -0.04M/s; C = 0.6 M/s; D = 0.04 mol/l s c) B= M/s; C= M/s; D= 0.04 mol/l s Consider the following reaction: N H 4(l) + H O (l) N (g) + 4H 0 (l) In.0 seconds, 0.05 mol of H O is consumed. The rate of production of N is A..5 x 0-3 mol/s B. 7.5 x 0-3 mol/s C. 6.0 x 0-3 mol/s D..5 x 0 - mol/s C3H8( g) 5O ( g) 3CO ( g) 4HO( g) Compared to the rate with respect to propane: Rate with respect to oxygen is five times faster Rate with respect to carbon dioxide is three times faster Rate with respect to water is four times faster Since the rates are all related any may be monitored to determine the reaction rate 3 4 6

7 /04/08 Quiz Determine relative reaction rates of the four substrates involved in the following chemical reaction. Give the appropriate numbers instead w, x, y and z letters: C H (g) + 5O (g) 4CO + H O (l) A reaction rate is generally not constant throughout the reaction. Since the most of reactions depend on the concentration of reactants, the rate changes as they are used up. The rate at any particular moment of given reaction is called the instantaneous rate. It can be calculated from a concentration versus time plot. 5 6 A plot of the concentration of HI versus time for the reaction:hi(g) H (g) + I (g). The slope is negative because we are measuring the disappearance of HI. When used to express the rate it is used as a positive number. 7 Plot of [H ] vs time for the reaction of.000 M H with.000 M ICl. The instantaneous rate of reaction at any time, t, equals the negative slope of the tangent to this curve at time t. The initial ratio of the reaction is equal to the negative of the initial slope (t=0). The determination of the instantaneous rate at t= second is illustrated. 8 7

8 concentration /04/08 Quiz Based on the graph below determine the instantaneous rate of change of [X] at 8 seconds A rate law is a mathematical equation that describes the progress of the reaction. In general, rate laws must be determined experimentally [X] =.. M/s Unless a reaction is an elementary reaction, it is not possible to predict the rate law from the overall chemical equation. There are two forms of a rate law for chemical kinetics: the differential rate law and the integrated rate law. 8 4 s time 9 30 For a generic reaction: reactant + reactant product with no intermediate steps in this reaction mechanism, the rate is given by Rate = k [reactant ] n [reactant ] m Rate constant, k rate = k [reactant ] n [reactant ] m where k is the constant of proportionality named rate constant. Its value is generally constant provided that reaction is performed at constant temperature T. Values of k are always positive, although it may be an exception of this rule

9 /04/08 Consider the following reaction: SeO 6I 4H Se I H From experiment, the rate law (determined from initial rates) is rate k[ H At 0 o C, k equals 5.0 x 0 5 L 5 mol -5 s - Thus, at 0 o C rate ( L 5 3 SeO3 ] [ I ] [ H ] mol -5 s ) [ H 3 H O SeO ][ I 3 ] [ H ] Order of reaction The exponent in a rate law is called the order of reaction with respect to the corresponding reactant. The exponents in the rate law are generally unrelated to the chemical equation s coefficients. Never simply assume that exponents and coefficients are the same. The exponents must be determined from the results of experiments For the rate law: rate k[ H 3 SeO3 ] [ I ] [ H ] We can say The reaction is first order with respect to H SeO 3 The reaction is third order with respect to I - The reaction is second order with respect to H + The reaction is sixth order overall Exponents (orders of reactions) in a rate law can be fractional, negative, and even zero. Reaction order quiz Analyse the following rate equations, and determine the orders of reaction with respect to reactant and overall reaction order:. rate = k [Cu + ] [NH 3 ]. rate = k [OH - ] 3. rate = k [NO] [O ] 4. rate = k [A] 3 [B]

10 /04/08 Determination of order of the reaction Looking for patterns in experimental data provide way to determine the exponents in a rate law. One of the easiest ways to reveal patterns in data is to form ratios of results using different sets of conditions. This technique is generally applicable. Consider the hypothetical reaction: A B products rate k[ A] m [ B] n Suppose the experimental concentrationrate data for five experiments is: Expt Inital Conc. [ A] (mol L ) (mol L ) (mol L s ) [ B] Initial Rate For experiments,, and 3 [B] is held constant, so any change in rate must be due to changes in [A] The rate law says that at constant [B] the rate is proportional to [A] m m rate [ A] rate [ A] - - rate 0.40 mol L s - - rate 0.0 mol L s m [ A] [ A] mol L mol L m m Thus m= For experiments 3, 4, and 5 [A] is held constant, so any change must be due to changes in [B] The rate law says that at constant [A] the rate is proportional to [B] n Using the results from experiment 3 and 4:

11 /04/08 rate [ B] 4 4 rate 3 [ B] 3 n n - - rate.40 mol L s rate mol L s - [ B] 0.0 mol L 4 n [ B] mol L 3 Thus n= The reaction is second order in respect to B and rate=k [A] [B] n The rate constant (k) can be determined using data from any experiment Using experiment : rate k [ A][ B] mol L s - (0.0 mol L )(0.0mol L ) L mol - Using data from a different experiment might give a slightly different value of k s For NO + O --> NO, initial rate data are: Quiz Experiment [NO] M/L [O ] M/L Rate [mm/ s] Quiz The reaction has the rate law: rate = k[c][d]. What will happen to the reaction rate when the following change in conditions is performed? doubling [C] tripling [D] Determine the reaction rates in terms of [NO], [O ] and k 43 44

12 /04/08 The relationship between concentration and time can be derived from the rate law and calculus. Integration of the rate laws gives the integrated rate laws, which present concentration as a function of time. Integrated laws can be very complicated, so only a few simple forms will be considered. In this reaction the speed of the reaction does not depend on the reagent concentrations. v = c t = kc0 = k v v k c 0 k v C C0 t tg a - k c photochemical reactions heterophaseous reaction in which the slowest process is connected with the phase change burning ethanol by living organism decomposition of ammonia synthesis of HCl from hydrogen and chlorine performed on the sun light t 47 48

13 /04/08 First order reaction Formula for the rate law is: rate = k [A] The integrate rate law can be expressed as: [ A] ln [ A] t kt or [ A] t [ A 0e 0 ] kt [A] 0 is [A] at t (time) = 0 [A] t is [A] at t = t e = base of natural logarithms =.788 First order reaction examples Absorption, distribution, elimination rates Microbial death kinetics Photo dissociation of ozone with UV light Decomposition of hydrogen peroxide at room temperature Hydrolysis of sucrose (sugar) to glucose and fructose e.g. SO Cl SO + Cl at 30 o C k = x 0-5 kj/ s C H 6 CH 3 at 700 o C k = 5.36 x 0-4 kj/ s Example of calculation For certain first-order reaction the initial concentration of reactant A is equal M/L and the rate constant of this reaction k = 0.5M/ L s. What is the concentration of A after time 6s? Quiz If a reaction is first order with a rate constant of 5.48 x 0 - sec -, how long is required for /4 of the initial concentration of reactant to be used up? Assume that initial concentration of reactant is equal to M. Or ln A 0 A t = kt; ln A 0 ln A 6 = kt = 0.83 M/L 5 5 3

14 /04/08 A plot of ln[a] t versus t gives a straight line with a slope of -k The decomposition of N O 5. (a) A graph of concentration versus time for the decomposition at 45 o C. (b) A straight line is obtained from a logarithm versus time plot. The slope is negative the rate constant. 53 Second order reaction The simplest second-order rate law has the form rate k[ B] The integrated form of this equation is [ B] [ B] [ B] t t 0 [ B] 0 kt the initial concentration of B the concentration of B at time t 54 Second order reaction examples Decomposition of HI without catalyst Decomposition of NO to NO and O ClO - + Br - BrO - + Cl - at 5 o C k = 4. x 0-7 kj/l mol - s - H + + OH - H O at 5 o C k =.35 x 0 kj/l mol - s - Graphical methods can also be applied to second-order reactions A plot of /[B] t versus t gives a straight line with a slope of k Second-order kinetics. A plot of /[HI] versus time

15 /04/08 Half life t / The amount of time required for half of a reactant to disappear is called the half-life, t / t = A 0 k For zero-order reactions, the half-life depends on the initial concentration of reactant and the rate constant The half-life of a first-order It is not affected by the initial concentration First- order rate law : at t t [ A] 0 ln [ A] /,[ A] 0 t kt / or t [ A] ln [ A] ln k t kt [ A] 0, substituti ng / 0 The half-life of a second-order reactions does depend on the initial concentration Second - order rate law : kt [ B] t [ B] 0 at t t/,[ B] t [ B] 0, substituti ng kt / [ B] 0 [ B] 0 ln kt/ or t/ [ B] 0 k[ B]

16 /04/08 () Graphical method Reagent concentration to t t t3 t4... co c c c3 c4... c c o n = 0 n = n = tg a - k t ln c ln c o tg a - k t c c tg a k c c k t ln c ln c k t k t c c t 6 63 Quiz Substance A decomposes by a first-order reaction. Starting initially with [A] =.00 M, after 50 min [A] = 0.50 M. What is t / for this reaction? First-order radioactive decay of iodine-3. The initial concentration is represented by [I]

17 concentration [mol /L] /04/08 Quiz 0 The table below presents plote of concentration of biologically active metabolite T-IDA vs time. Using of these data determine graphically the half-time life (t / ) of this metabolite Time [min] Concentra tion [mol /L] , Time [min] 66 T / = 0 min 67 There are five principle factors that influence reaction rates: ) Chemical nature of the reactants ) Ability of the reactants to come in contact with each other 3) Concentration of the reactants 4) Temperature 5) Availability of rate-accelerating agents called catalysts Chemical nature of the reactants Bonds break and form during reactions The most fundamental difference in reaction rates lies in the reactants themselves. Some reactions are fast by nature whereas others are slow C (diamond) + O (g) CO (g) ΔG 0 rxn = -397 kj/mol This reaction one does not occur. C (graphite) + O (g) CO (g) ΔG 0 rxn = -394 kj/mol. This reaction occurs rapidly Diamond structure Graphite structure 70 7

18 /04/08 Ability of the reactants to meet Most reactions require that particles (atoms, molecules, or ions) collide before the reaction can occur. This depends on the phase of the reactants. In a homogeneous reaction the reactants are in the same phase: For example both reactants in the gas (vapour) phase. In a heterogeneous reaction the reactants are in different phases: For example one reactant is present in the liquid whereas the second is in the solid phase. In heterogeneous reactions the reactants meet only at the intersection between the phases. Thus the area of contact between the phases determines the rate of the reaction. 7 7 Concentration of the reactants Effect of crushing a solid. When a single solid is subdivided into much smaller pieces, the total surface area on all of the pieces becomes very large. Both homogeneous and heterogeneous reaction rates are affected by reactant concentration

19 /04/08 H O (aq) H O (l) + ½ O (g) Volume O [cm 3 ] 0.5 mol/l of H O 0.4 mol/l 0.3 mol/l 0. mol/l 0. mol/ l Time [s] Temperature The rates for almost all chemical reactions enhance as the temperature is increased Cold-blooded creatures, such as insects and reptiles, become sluggish at lower temperatures as their metabolism slows down

20 /04/08 In experiments it was determined that in homogenous reaction temperature enhancement of 0 o results -4 times increasing of reaction speed. Increase of temperature cause increase of rate constant (k) in rate law. Number describing how many times k increases is known as temperature coefficient (θ). According to the van't Hoff rule Q = k k T T The rate of a chemical reaction doubles for every 0 C rise of temperature. If the temperature is raised by 50 C, the rate of the reaction increases by about: a) 0 Times; b) 4 Times; c) 3 Times; d) 64 times. If temperature increases from 0 o C to 50 o C the velocity of reaction increases in 8 times. What the temperature coefficient is equal to? A) 8; b) 4; c) 3; d) Example Consider this reaction: Zn (s) + HCl (aq) ZnCl (aq) + H (g)

21 /04/08 Condition Affect on Rate Explanation Concentration Increasing the More HCl particles means there concentration of HCl will will be more collisions between increase the reaction rate. HCl and Zn. Condition Affect on Rate Explanation Particle Size Reducing the size of Zn particles will increase the rate of reaction. Reducing the size of the Zn particles increases the surface area available for reaction with HCl molecules resulting in more collisions. Temperature Increasing temperature increases the reaction rate. HCl particles will gain more kinetic energy increasing the number of collisions with Zn atoms. More Zn and HCl particles will have sufficient energy to react resulting in more successful collisions. Stirring Rate Stirring will keep small Zn particles Increasing the in suspension, increasing the stirring rate of this surface area available for mixture will increase collisions, resulting in an increased the reaction rate. reaction rate Quiz Student performed experiment on dissolution of Mg in HCl in four test tubes according to the following conditions. Test tube Mg size HCl concentration cube.0 M cube 0.5 M 3 powder.0 M 4 powder 0.5 M A catalyst is a substance that changes the rate of a chemical reaction without itself being used up. Positive catalysts speed up reactions Negative catalysts or inhibitors slow reactions (Positive) catalysts speed reactions by allowing the rate-limiting step to proceed with a lower activation energy. Thus a larger fraction of the collisions is effective. Determine the order of test tubes according to the reaction time decreasing 85 86

22 /04/08 (a) The catalyst provides an alternate, low-energy path from the reactants to the products. (b) A larger fraction of molecules have sufficient energy to react when the catalyzed path is available. Catalysts can be divided into two groups Homogeneous catalysts exist in the same phase as the reactants. Heterogeneous catalysts exist in a separate phase. NO is a homogeneous catalyst for the production of sulfuric acid in the lead chamber process. The mechanism is: SO SO S O O SO H O H SO 3 4 The second step is slow, but is catalyzed by NO : NO NO SO SO 3 NO SO O NO 3 Heterogeneous catalysts are typically solids Consider the synthesis of ammonia from hydrogen and nitrogen by the Haber process 3H N NH

23 /04/08 The Haber process. Catalytic formation of ammonia molecules from hydrogen and nitrogen on the surface of a catalyst Mechanism theories

24 /04/08 The reaction s mechanism is the series of simple reactions called elementary processes. The rate law of an elementary process can be written from its chemical equation. One of the simplest models explaining reaction rates is collision theory. According to collision theory, the rate of reaction is proportional to the effective number of collisions per second among the reacting molecules. An effective collision is one that actually gives product molecules. The number of all types of collisions increase with concentration, including effective collisions There are a number of reasons why only a small fraction of all the collisions leads to the formation of product: Only a small fraction of the collisions are energetic enough to lead to products. Molecular orientation is important because a collision on the wrong side of a reacting species cannot produce any product. This becomes more important as the complexity of the reactants increases. The key step in the decomposition of NO Cl to NO and Cl is the collision of a Cl atom with a NO Cl molecules. (a) A poorly orientated collision. (b) An effectively orientated collision

25 /04/08 The minimum of kinetic energy of the colliding particles must have is called the activation energy, E a. In a successful collision, the activation energy changes to potential energy as the bonds rearrange to for products. Activation energies can be large, so only a small fraction of the well-orientated, colliding molecules have it. When temperature increases the average kinetic energy of the reacting particle also increases. 00 Kinetic energy distribution for a reaction at two different temperatures. At the higher temperature, a larger fraction of the collisions have sufficient energy for reaction to occur. The shaded area under the curves represent the reacting fraction of the collisions. 0 The potential-energy diagram for an exothermic reaction. The extent of reaction is represented as the reaction coordinate. 0 A unsuccessful (a) and successful (b) collision for an exothermic reaction

26 /04/08 Activation energies and heats of reactions can be determined from potential-energy diagrams Potential-energy diagram for an endothermic reaction. The heat of reaction and activation energy are labeled. Reactions generally have different activation energies in the forward and reverse direction Activation energy barrier for the forward and reverse reactions The brief moment during a successful collision that the reactant bonds are partially broken and the product bonds are partially formed is called the transition state. Transition state theory explains what happens when reactant particles come together. 0 6 Formation of the activated complex in the reaction between NO Cl and Cl. NO Cl+ClNO +Cl 0 7 6

27 /04/08 The overall rate law determined for the mechanism must agree with the observed rate law. The exponents in the rate law for an elementary process are equal to the coefficients of the reactants in chemical equation Elementary process: NO NO rate k[no 3 ] NO Multistep reactions are common. The sum of the elementary processes must give the overall reaction. The slowest set in a multistep reaction limits how fast the final products can be formed and is called the rate-determining or rate-limiting step. Simultaneous collisions between three or more particles are extremely rare A reaction that depended on a three-body collision would be extremely slow. Thus, reaction mechanism seldom includes elementary process that involves more than two-body or bimolecular collisions. Consider the reaction NO H N H O rate k[no] [H ] (experimental) The mechanism is thought to be N O NO H N O H N N O H O N O H O (fast) (slow) (fast) The second step is the rate-limiting step, which gives rate k[no][h] N O is a reactive intermediate, and can be eliminated from the expression. 0 7

28 /04/08 The first step reaches a fast equilibrium At equilibrium, the rate of the forward and reverse reaction are equal rate(forward) k rate(reverse) k [N O ] f k [NO] k f r r r f [NO] [NO] k [NO] k [N O ] or thus Substituting, the rate law becomes rate k[n O k rate k k ][H [NO] [H rate k'[no] [H f r ] or Which is consistent with the experimental rate law. ] ] 3 The activation energy is related to the rate constant by the Arrhenius equation / RT k Ae E a k = rate constant E a = activation energy e = base of the natural logarithm R = gas constant = 8.34 J mol - K - T = Kelvin temperature A = frequency factor or pre-exponential factor The activation energy can be related to the rate constant at two temperatures k ln k E a R T T 4 5 8

29 /04/08 Quiz The activation energy of the first order reaction is 50, kj/mol at 5 o C. At what temperature will the rate constant double?

30 /04/08 True or false quiz. A catalyst alters the rate of a chemical reaction by: a) always providing a surface on which molecules react b) changing the products formed in the reaction c) inducing an alternate pathway for the reaction with generally lower activation energy d) changing the frequency of collisions between molecules. The Rate of a Chemical Reaction a) usually is increased when the concentration of one of the reactants is increased b) is dependent on temperature c) may be inhibited by certain catalytic agents d) will be very rapid if the activation energy is large 0 30