Chapter 22. The rates of chemical reactions

1. Chapter 22. The rates of chemical reactions

2. 22.1 Experimental techniques • Monitoring concentrations: Depends on the species involved and the rapidity with which their concentrations changes. 1. spectrophotometry. 2. electrical conductivity 3. pH of the solution 4. redox potential • Determining the compositions of a solution: 1. mass spectrometry 2. gas chromatography 3. emission spectroscopy 4. nuclear magnetic resonance 5. electron spin resonance

3. Flow method

4. Stopped flow method

5. Additional techniques • Flash photolysis. (principles…) • Quenching methods: 1. Chemical Quenching method. 2. Freezing quenching method.

6. 22.2 The rates of reactions • The definition of the rate A + 2B → 3C + D The rate of consumption of one of the reactants (R) at a given time is - , where R could be reagent A or B.

7. The rate of formation of one of the products (denoted by P) is • Following the stoichiometry of the above reaction, one gets

8. Rate of reaction • Defined as the rate of change of the extent of reaction, ξ. • Since the change in the extent of reaction is related to the change in the amount of each substance J by • When expressed in term of concentration: note that vjis negative for reactants and positive for products!

9. Example: The rate of change of molar concentration of CH3 radicals in the reaction 2CH3(g) → CH3CH3(g) was reported as d[CH3]/dt = 1.2 mol L-1s-1 under particular conditions. What is (a) the rate of reaction and (b) the rate of formation of CH3CH3? • Solution:

10. Rate laws and rate constant • A rate law is often expressed as a function v = k [A] [B] where k is called rate constant. • In general, rate law cannot be inferred from the chemical reaction equation. Example: H2(g) + Br2(g) → 2HBr(g)

11. Reaction order • The rate law can be written in a generalized form: v = k [A]a[B]b…. where a is the order of the reaction with respect to the species A, and b is the order of the reaction with respect to the species B. • The overall reaction order is (a+b+….). • The order of a chemical reaction needs not to be an integral !!! Example 1: v = k [A]1/2[B]1 Example 2: v = k (zero order reaction, such as ……)

12. Determination of the rate law • Isolation method: v = k [A]a[B]b -----> v = k’[B]b • Method of initial rates: v = k [A]a at the beginning of the reaction v = k [A0]a taking logarithms gives: logv = log k + a log[A0] therefore the plot of the logarithms of the initial rates against the logarithms of the initial concentrations of A should be a straight line with the slope a (the order of the reaction).

13. Example: The initial rate of a reaction depended on the concentration of a substance B as follows: [B]0/(mmol L-1) 5.0 8.2 17 30 v0/(10-7 mol L-1s-1) 3.6 9.6 41 130 Determine the order of the reaction with respect to B and calculate the rate constant. Solution: Log([B]0) -2.30 -2.086 -1.770 -1.523 Log(v0) -6.444 -6.018 -5.387 -4.886

14. 22.3 Integrated rate law • First order reaction: A  Product The solution of the above differential equation is: or: [A] = [A]0e-kt • In a first order reaction, the concentration of reactants decreases exponentially in time.

15. Example:In a particular experiment, it was found that the concentration of N2O5 in liquid bromine varied with time as follows: t/s 0 200 400 600 1000 [N2O5]/(mol L-1) 0.110 0.073 0.048 0.032 0.014 confirm that the reaction is first-order in N2O5 and determine the rate constant. Solution:To confirm that a reaction is first order, plot ln([A]/[A]0) against time and expect a straight line: t/s 0 200 400 600 1000 ln([A]/[A]0) 0 -0.410 -0.829 -1.23 -2.06

16. Half-lives and time constant • For the first order reaction, the half-live equals: therefore, is independent of the initial concentration. • Time constant, τ, the time required for the concentration of a reactant to fall to 1/e of its initial value. for the first order reaction.