CHAPTER 13: CHEMICAL KINETICS RATE LAWS FIRST ORDER REACTIONS

Reaction Rate: Concentration-Rate Law Rate Law for Equation with One Reactant: A  products Rate = k [A] m Rate Law for Equation with Two Reactants A + B  Products Rate = k[reactant 1] m [reactant 2] n “k” is the rate law constant; temperature related “m” and “n” are rate law exponents

Reaction Rate: Concentration-Rate Law To Deduce Intuitively Rate Law Exponents: From data, observe correlation between change in concentration and rate. rate law exponent is zero (zero order) for a reactant if the change in concentration of that reactant produces no effect. Rate law exponent is one (first order) if doubling the concentration causes the rate to double.

To Deduce, Intuitively, Rate Law Exponents: Rate law exponent is two (second order) if doubling the concentration results in a 2 2 increase in rate. Note that the rate constant does not depend on concentration.

Reaction Rate: Concentration NH 4 + (aq) + NO 2 - (aq)  N 2 (g) + 2H 2 O(l)

Algebraic Determination of Rate Law Exponents 1. Chose two experiments. 2. Compare rates and concentrations rate 2 /rate 1 =( [A] 2 /[A] 1 ) n

Algebraic Determination of Rate Law Exponents 1. Choose Experiments 1 and 2 rate 2 /rate 1 =( [A] 2 /[A] 1 ) n 10.8E-7/5.4E-7 = ( 0.200/0.100) n 2 = (2) n

Problem a, b (9 th Edition) The reaction 2ClO 2 (aq) + 2OH - (aq)  ClO 3 - (aq) + ClO 2 - (aq) + H 2 O (l) was studied with the following results. Exp[ClO 2 ] [OH - ] Rate (M/s)

Problem a, b (9 th Edition) (a) Determine the rate law (b) Calculate the value of the rate law constant

Problem 13.20: page 604 Kinetics data was collected for the reaction given below. Determine the order of the reaction and the rate constant. T = 290 °C ClCO 2 CCL 3 (g)  2COCl 2 (g) TIME (s)P (mmHg)

Rate Laws: General Comments Write rate laws for ELEMENTARY REACTIONS –Unimolecular –A  B –Bimolecular –A + B  Products

Rate Laws: General Comments UNIMOLECULAR REACTIONS –DECOMPOSITION – 2N 2 O 5  4NO 2 + O 2 –REARRANGEMENT – CH 2 –  CH 3 CH=CH 2 – CH 2 CH 2

Rate Laws: General Comments REACTION ORDER –RATE = [A] 1 –RATE = [A] 2 –RATE = [A] [B] –RATE =[A] 0

Effect of Concentration: Rate Laws First-Order Reactions rate = k[A] 1 A plot of ln[A] t versus t is a straight line with slope -k and intercept ln[A] 0.

The Change of Concentration with Time Half-Life

Problem ….The decomposition of sulfuryl choride (SO 2 Cl 2 ) is a first order process. The rate constant for the decomposition at 660 K is 4.5E-2s -1. (a) If we begin with an initial SO 2 Cl 2 pressure of 375 torr, what is this pressure after 65 seconds.

Problem ln[A] t = -kt +ln [A] 0 4.5E-2s -1 [A] t = ? [A] 0 = 375 torr ln (x) = -(4.5E-2s -1 )(65 seconds) + (ln 375) ln (x) = = inverse/antilog/e x = 20.1 torr

Reaction Rate & Concentration: First Order Reactions The first-order rate constant for the decomposition of an antibiotic is 6.82E-3 hour –1. The initial concentration of the antibiotic is 125 mg. How long will it take for the antibiotic to decompose to 25.0 mg?

Effect of Concentration: Rate Laws First Order Reactions and Half-Life Half-life is the time taken for the concentration of a reactant to drop to half its original value. That is, half life, t 1/2 is the time taken for [A] 0 to reach ½[A] 0. Mathematically,

First Order Reactions: Half-Life The first-order rate constant for the decomposition of an antibiotic is 6.82E-3 hour –1. Calculate the half-life for this antibiotic.

Effect of Concentration: Rate Laws First-Order Reactions

Reaction Rate: Concentration Second-Order Reactions: rate = k [A] rate = k [A] [B] For a second order reaction with just one reactant A plot of 1/[A] t versus t is a straight line with slope k and intercept 1/[A] 0 For a second order reaction, a plot of ln[A] t vs. t is not linear.

The Change of Concentration with Time Second-Order Reactions

The Change of Concentration with Time Second-Order Reactions We can show that the half life A reaction can have rate constant expression of the form rate = k[A][B], i.e., is second order overall, but has first order dependence on A and B.

Table 13.3

Problem The decomposition of hydrogen iodide follows the equation 2HI (g)  H 2(g) + I 2(g). The reaction is second order and has a rate constant equal to 1.6E- 3 L mole -1 s -1 at 700 Celsius degrees. If the initial concentration of HI in a container is 3.4E-2 M, how many minutes will it take for the concentration to be reduced to 8.0E-4 M?