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14-4 Zero-Order Reactions

14-4 Zero-Order Reactions. A → products. R rxn = k [A] 0. R rxn = k. [ k ] = mol L -1 s -1. -d[A]. Move to the infinitesimal. = k. d t. t. [A] t. - . . d[A]. = k. d t. [A] 0. 0. Integrated Rate Law. - Δ [A]. = k. Δ t. And integrate from 0 to time t.

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14-4 Zero-Order Reactions

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  1. 14-4 Zero-Order Reactions A → products Rrxn = k [A]0 Rrxn = k [k] = mol L-1 s-1

  2. -d[A] Move to the infinitesimal = k dt t [A]t -  d[A] = k dt [A]0 0 Integrated Rate Law -Δ[A] = k Δt And integrate from 0 to time t -[A]t+ [A]0= kt [A]t = [A]0 - kt

  3. d[H2O2 ] = - k dt [H2O2] [A]t ln = -kt ln[A]t= -kt + ln[A]0 t [A]t [A]0   [A]0 0 14-5 First-Order Reactions H2O2(aq) → H2O(l) + ½ O2(g) d[H2O2 ] = -k[H2O2] [k] = s-1 dt

  4. First-Order Reactions

  5. [A]t ln = -kt [A]0 ½[A]0 ln = -kt½ [A]0 ln 2 0.693 t½ = = k k Half-Life • t½ is the time taken for one-half of a reactant to be consumed. - ln 2 = -kt½

  6. Half-Life ButOOBut(g) → 2 CH3CO(g) + C2H4(g)

  7. Some Typical First-Order Processes

  8. [k] = M-1 s-1 = L mol-1 s-1 d[A] = -k[A]2 dt d[A] = - k dt [A]2 t [A]t 1 1   = kt + [A]t [A]0 [A]0 0 14-6 Second-Order Reactions • Rate law where sum of exponents m + n +… = 2. A → products

  9. Second-Order Reaction

  10. Testing for a Rate Law Plot [A] vs t. Plot ln[A] vs t. Plot 1/[A] vs t.

  11. 14-7 Reaction Kinetics: A Summary • Calculate the rate of a reaction from a known rate law using: • Determine the instantaneous rate of the reaction by: Rate of reaction = k [A]m[B]n …. Finding the slope of the tangent line of [A] vs t or, Evaluate –Δ[A]/Δt, with a short Δt interval.

  12. Summary of Kinetics • Determine the order of reaction by: Using the method of initial rates. Find the graph that yields a straight line. Test for the half-life to find first order reactions. Substitute data into integrated rate laws to find the rate law that gives a consistent value of k.

  13. Summary of Kinetics • Find the rate constant k by: • Find reactant concentrations or times for certain conditions using the integrated rate law after determining k. Determining the slope of a straight line graph. Evaluating k with the integrated rate law. Measuring the half life of first-order reactions.

  14. Worked Examples Follow:

  15. CRS Questions Follow:

  16. ln [X] t In the diagram to the right is a plot of the concentrations of all reactants and products as a function of time for a particular reaction. Which of the following statements is correct? 1. The reaction is second order. 2. The blue curve represents the time dependence on a particular product. 3. The rate constant for the reaction could have units of s-1. 4. The product represented by the green line is produced almost twice as fast as the product represented by the red line. 5. Cannot tell with the information given.

  17. ln [X] t In the diagram to the right is a plot of the concentrations of all reactants and products as a function of time for a particular reaction. Which of the following statements is correct? 1. The reaction is second order. 2. The blue curve represents the time dependence on a particular product. 3. The rate constant for the reaction could have units of s-1. 4. The product represented by the green line is produced almost twice as fast as the product represented by the red line. 5. Cannot tell with the information given.

  18. ln [X] t In this question, two reactions are considered. Reaction A has a rate constant which is equal to 16.2 L mol-1 s-1. A plot relating the concentrations of the reactants and products with time is plotted for reaction B to the right. • Reaction A is first order and Reaction B is second order. 2. Reaction A is second order and Reaction B is first order. 3. Both reactions are first order. 4. Both reactions are second order.

  19. ln [X] t In this question, two reactions are considered. Reaction A has a rate constant which is equal to 16.2 L mol-1 s-1. A plot relating the concentrations of the reactants and products with time is plotted for reaction B to the right. • Reaction A is first order and Reaction B is second order. 2. Reaction A is second order and Reaction B is first order. 3. Both reactions are first order. 4. Both reactions are second order.

  20. 81.7 s 81.7 s 81.7 s Some data for the decomposition of dinitrogen pentoxide are plotted to the right. Which of the following statements is correct? 1. The rate constant is 81.7 s. 2. The rate constant is 3. The units of the rate constant are s. 4. The reaction is first order in N2O5. 5. The reaction is third order in N2O5.

  21. 81.7 s 81.7 s 81.7 s Some data for the decomposition of dinitrogen pentoxide are plotted to the right. Which of the following statements is correct? 1. The rate constant is 81.7 s. 2. The rate constant is 3. The units of the rate constant are s. 4. The reaction is first order in N2O5. 5. The reaction is third order in N2O5.

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