Reaction Rates and Rate Laws

1. Reaction Rates and Rate Laws Chapter 14

2. Reaction Rates Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time.

3. Reaction Rates In this reaction, the concentration of butyl chloride, C4H9Cl, was measured at various times. C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

4. Reaction Rates The average rate of the reaction over each interval is the change in concentration divided by the change in time: Average rate = [C4H9Cl] t C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

5. Reaction Rates Note that the average rate decreases as the reaction proceeds. This is because as the reaction goes forward, there are fewer collisions between reactant molecules because there are not as many reactants left to collide C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

6. Reaction Rates A plot of concentration vs. time for this reaction yields a curve like this. The slope of a line tangent to the curve at any point is the instantaneous rate at that time. Instantaneous rate = change in conc./change in time C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

7. Reaction Rates All reactions slow down over time. Therefore, the best indicator of the rate of a reaction is the instantaneous rate near the beginning. C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

8. Reaction Rates and Stoichiometry In this reaction, the ratio of C4H9Cl to C4H9OH is 1:1. Thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH. -[C4H9Cl] t Rate = = [C4H9OH] t C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

9. Reaction Rates and Stoichiometry What if the ratio is not 1:1? aA + bB cC + dD 1 2 = = Rate = − = − [HI] t Rate = − = 1 b 1 c 1 d 1 a [D] t [C] t [A] t [B] t [I2] t 2 HI(g) H2(g) + I2(g) • Therefore, • To generalize, then, for the reaction

10. = = Rate = − = − 1 a 1 b 1 c 1 d [C] t [D] t [A] t [B] t Practice Problem • How is the rate at which ozone disappears related to the rate at which oxygen appears in the reaction: 2O3(g)  3O2(g) Rate= -1/2*Δ[O3]/ Δt = 1/3 Δ[O2]/ Δt

11. Practice Problem 2 If the rate at which O2 appears, Δ[O2]/ Δt, is 6.0 x 10-5 M/s at a particular instant, at what rate is O3 disappearing at this same time, -Δ[O3]/ Δt ? Rate= -1/2*Δ[O3]/ Δt = 1/3 Δ[O2]/ Δt Rate = - Δ[O3]/ Δt = 2/3 * (6.0 x 10-5) Rate = 4.0 x 10-5 M/s

12. Concentration and Rate One can gain information about the rate of a reaction by seeing how the rate changes with changes in concentration for each reactant.

13. Concentration and Rate Comparing Experiments 1 and 2, when [NH4+] doubles, the initial rate doubles. N2(g) + 2 H2O(l) NH4+(aq) + NO2−(aq)

14. Concentration and Rate Likewise, comparing Experiments 5 and 6, when [NO2−] doubles, the initial rate doubles. N2(g) + 2 H2O(l) NH4+(aq) + NO2−(aq)

15. Concentration and Rate This means Rate  [NH4+] Rate  [NO2−] Rate  [NH+] [NO2−] or Rate = k [NH4+] [NO2−] This equation is called the rate law, and k is the rate constant. Rate = k[A]m[B]n

16. Rate constant, k • k is temperature dependent, k increases with increasing temperature (reaction rates increase with temperature) • Rate constants can vary over many orders of magnitude because reaction rates vary widely

17. Rate Laws A rate law shows the relationship between the reaction rate and the concentrations of reactants. The exponents tell the order of the reaction with respect to each reactant. Rate = k [NH4+] [NO2−] This reaction is First-order in [NH4+] First-order in [NO2−]

18. Rate Laws The overall reaction order can be found by adding the exponents on the reactants in the rate law. Rate = k [NH4+] [NO2−] This reaction is second-order overall.

19. Rate Laws • Although the exponents in rate laws are sometimes the same as the coefficients in the balanced equation, this is not necessarily the case. • If the reaction occurs in more than one step the rate law cannot always be expressed this way • The values of these exponents must be determined experimentally by looking at the rate at which that reactant changes over time

20. What is the overall rate reaction orders for each reaction? 2 N2O5(g)  4NO2(g) + O2(g) Rate= K[N2O5] • First order CHCl3 + Cl2  CCl4(g) + HCl(g) Rate= k[CHCl3][Cl2]1/2 • 3/2 order H2(g) + I2(g)  2HI(g) Rate= k[H2][I2] • Second order

21. Determining a Rate Law from Initial Rate Data The initial rate of a reaction A + B  C was measured for several different starting concentrations of A and B, and the results are as follows: Using these data, determine (a) the rate law for the reaction (b) the rate constant (c) the rate of the reaction when [A] = 0.050 M and [B] = 0.100 M

22. Determine the rate law for the reaction Rate = k[A]m[B]n Experiment 1 and 2: [A] stays the same, [B] doubles but has no effect on the rate (so zero order for [B]) Experiment 1 & 3: [A] doubles, and rate quadruples while [B] remains the same, so therefore A is a second order reaction [A]2 Therefore, rate= k[A]2, so second order overall

23. Determine the rate constant Rate = k[A]2 k= (4.0 x 10-5 M/s)/ (0.100 M)2 k= 4.0 x 10-3 M-1s-1

24. Determine the rate of the reaction when [A] = 0.050 M and [B] = 0.100 M Rate =4.0 x 10-3 M-1s-1 x (0.050) 2 Rate = 1.05 x 10-5 M/s