Chemical Kinetics PDF

Chemical kinetics Chemical kinetics deals with the speed with which a chemical reaction occurs. The rate of reaction refers to the rate of change of concentration of the reactant or product with respect to time. Consider the reaction A + B C + D The rate of consumption of A or B = rat...

Chemical kinetics Chemical kinetics deals with the speed with which a chemical reaction occurs. The rate of reaction refers to the rate of change of concentration of the reactant or product with respect to time. Consider the reaction A + B C + D The rate of consumption of A or B = rate of formation of C and D. Mathematically, it is written as 𝑑[𝐴] 𝑑[𝐵] 𝑑[𝐶] 𝑑[𝐷] R=− =− = = 1.1 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 The negative sign shows that the reactant is consumed while the positive sign shows that product is formed. Also, given that a A + b B cC + dD The instantaneous rate (the rate of reaction at one moment in time) is given by 1 𝛥[𝐴] 1 𝛥[𝐵] 1 𝛥[𝐶] 1 𝛥[𝐷] R=− =− = = 1.2 𝑎 𝑑𝑡 𝑏 𝑑𝑡 𝑐 𝑑𝑡 𝑑 𝑑𝑡 Factors Affecting Rate of Reaction 1. Concentration: Reaction rate increases with increase in concentration due to increase in the frequency of effective collision of reacting molecules. 2. Surface Area: Increase in the surface area increases the number of reaction sites. Increasing the reaction sites increases the total number of effective collision and consequently the rate of reaction. 3. Temperature: Increase in temperature increases the rate of reaction. At higher temperature the fraction of molecules with energies greater than the activation energy increases. Thus a greater number of the reacting molecules are able to form product. 4. Catalyst: The presence of catalyst increases the rate of chemical reaction. It reduces the activation energy by providing an alternative pathway for the reactant to form product. RATE LAWS Rate laws are mathematical equations which show the relationship between the rate of reaction and the concentrations of the reactants. Consider the reaction aA + bB cC + dD The rate law is given by R = k [A]m[B]n 1.3 [A] and [B] are the concentrations of reactants A and B, k is the rate constant, which is specific to a reaction. m and n are not the stoichiometric values (a and b).. m is the order of reactant A while n is the order of reactant B. The overall order of the reaction is given by the sum of the orders m + n The rate constant, and orders of a reaction are determined experimentally. The rate constant is independent of the concentration of the reactant but dependent on the temperature of the reaction. The rate law of a reaction is therefore determined experimentally, and in general cannot be obtained from the chemical equation for the reaction. For example, the reaction of hydrogen and bromine, has a very simple stoichiometry, H2(g) + Br2(g) → 2HBr(g), but its rate law is complicated and is given by 3 k[ H 2 ][ Br2 ] 2 R 1.4 [ Br2 ]  k ' [ HBr ]  The order of a reaction is the power to which each concentration term of the reactant is raised to show the correct dependence of rate on concentration. There are different orders of reactions: first order, second order, third order, zero order and fractional order. For example, consider the rate law 1 𝑅 = 𝑘[𝐴]2 [𝐵] 1.5 The order of reactant A is ½ while the order of reactant B is 1. The overall order is 3/2. There can also be negative orders Determination of rate laws 1. Isolation method This is the method in which the concentrations of all the reactants except one are in large excess. If A is in large excess, then its concentration is approximately constant throughout the reaction. Although the true rate law might be R=k[A][B] 1.6 we can approximate [A] by [A] = [A]o So that R=k′[B] where k′=k[A] 1.7 Eq. 1.7 has the form of a first-order rate law. It can be seen that the true rate law (eq.1.6) has been forced into first-order form by assuming that the concentration of A is constant, eqn 1.7 is called a pseudo-first-order rate law. The dependence of the rate on the concentration of each of the reactants may be determined by isolating them in turn (by having all the other substances present in large excess), thereby obtaining the overall rate law. Examples of pseudo-first order reactions include 1. Hydrolysis of an ester: The acid hydrolysis of ethyl acetate to give acetic acid and ethanol. CH3COOC2H5 + H2O CH3COOH + C2H5OH Ethyl acetate (excess) acetic acid ethanol(ethyl alcohol) The water (H2O) is in large excess such that the rate law can be written as R = k[CH3COOC2H5][ H2O] = k’[CH3COOC2H5] The reaction is actually supposed to be a second order but in practice due to the large excess of H2O, it is found to be a first order. Thus, the reaction is a pseudo- first order. 2. Hydrolysis of sucrose in the presence of a dilute mineral acid yields glucose and fructose. C12H22O11 + H2O C6H12O6 + C6H12O6 Sucrose (excess) glucose fructose Since the concentration of water [H2O] is practically constant because it is in excess, the rate law can be given by R = k[C12H22O11][ H2O] =k’[C12H22O11] The reaction, though a second order, is found experimentally to be first order. Hence it is a pseudo-first order reaction. 2. Initial rate method, This method is often used with the isolation method. Measurement of the rate is carried out at the commencement of the reaction for several different initial concentrations of reactants. Consider a rate law for a reaction with B isolated given by R = k[B]b 1.8 then its initial rate, Ro, is given by the initial values of the concentration of B, and we write Ro = k[B]ob 1.9 If we take the logarithms of both sides, we have log Ro = log k + b log [B]o 1.10 For a series of initial concentrations, a plot of the logarithms of the initial rates Ro against the logarithms of the initial concentrations of B would be a straight line with slope b and the intercept is log k. (iii) Integral methods Because rate laws are differential equations, we must integrate them if we want to find the concentrations as a function of time. In order words, one can measure the concentrations as a function of time, and compare their time dependence with the appropriate integrated rate laws. This approach easily simplifies the rate law so that it depends on only one reactant concentration. The integrated rate laws include Zeroth order integrated rate law: [X] = [X]o – kt A plot of [X] vs t will be linear, with a slope of –k and intercept [X]o First order integrated rate law: ln[X] = ln[X]o – kt A plot of ln[X] vs t will be linear with a slope of –k and intercept [X]o Second order integrated rate law: 1 1 = + 2𝑘𝑡 [𝑋] [𝑋]𝑜 1 1 A plot of against t will give a straight line whose slope is 2k and intercept is. [𝑋] [𝑋]𝑜 Third order integrated rate law 1 1 = + 2𝑘𝑡 [𝑋]2 [𝑋]2𝑜 1 1 A plot of against t will give a straight line whose slope is 2k and intercept is. [𝑋]2 [𝑋]2𝑜 (iv) Half lives The behaviour of the half -life as the reaction proceeds is a method of determining the reaction order. A number of successive half- lives, t = 0 is used at the commencement of the reaction at time t from which to measure the first half life, t1/2, the second half life t1/2 and so on. For zeroth order, 𝑡1=[𝑋]𝑜 2 2𝑘 For a zeroth order reaction, at the first t1/2, the original concentration [X]o is reduced by half. Thus successive half - lives will reduce by a factor of 2. First order 𝑙𝑛2 𝑡1 = 2 𝑘 The half -life of a second order reaction is independent on the concentration of the reactant. Hence its half- life is constant. Second order 1 𝑡1 = 2 𝑘[𝑋]𝑜 The half-life of a second order reaction is inversely proportional to the concentration of the reactant. Third order 3 𝑡1 = 2 2𝑘3 [𝑋]2𝑜 The half-life of a third order reaction is inversely proportional to the square of the concentration of the reactant. In general, for an n-th order reaction X P the half-life is related to the rate constant and the initial concentration of X by  1 𝑡1 = 2 𝑘[𝑋]𝑛−1 Reference 1. Atkins P. and de Paula J. 2006. Physical Chemistry. 8th Ed. Freeman and Company. 2. Bahl, B.S, Bahl A, Tuli G.D. Essentials of Physical Chemistry. S Chand and Company Ltd.