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Chapter 14: Problem 11

The initial rate of the reaction \(A+B \longrightarrow C+D\) is determined for different initial conditions, with the results listed in the table. (a) What is the order of reaction with respect to A and to B? (b) What is the overall reaction order? (c) What is the value of the rate constant, \(k ?\) $$\begin{array}{llll} \hline \text { Expt } & \text { [A], M } & \text { [B], M } & \text { Initial Rate, M s }^{-1} \\ \hline 1 & 0.185 & 0.133 & 3.35 \times 10^{-4} \\ 2 & 0.185 & 0.266 & 1.35 \times 10^{-3} \\ 3 & 0.370 & 0.133 & 6.75 \times 10^{-4} \\ 4 & 0.370 & 0.266 & 2.70 \times 10^{-3} \\ \hline \end{array}$$

Short Answer

Expert verified
The order of reaction with respect to A is 1, with respect to B is 2. Thus, overall reaction order is 3. The rate constant k can be calculated by substituting in the rate law the values from any experiment.

Step by step solution

01

Determine order of reaction with respect to A

To find the order of reaction with respect to 'A', compare Experiments 1 and 3. The concentration of 'B' is constant and the concentration of 'A' doubles from Experiment 1 to 3 ([A] in Expt. 3 = 2 × [A] in Expt. 1). Meanwhile, the initial rate also doubles (Rate in Expt. 3 = 2 × Rate in Expt. 1). Therefore, the order of reaction with respect to A is 1.
02

Determine order of reaction with respect to B

To find the order of reaction with respect to 'B', compare Experiments 1 and 2. The concentration of 'A' is constant while 'B' doubles from Experiment 1 to 2 ([B] in Expt. 2 = 2 × [B] in Expt. 1). The initial rate shows a four-fold increase (Rate in Expt. 2 = 4 × Rate in Expt. 1). Therefore, the order of reaction with respect to B is 2.
03

Identify the overall reaction order

The overall reaction order is simply the sum of the individual reaction orders. Thus, the overall order of reaction = order wrt A + order wrt B = 1 + 2 = 3.
04

Calculation of the rate constant k

Use the rate law and data from any of the experiments (e.g., Experiment 1) to calculate the rate constant. The rate law is given by rate = \(k[A]^m[B]^n\), where m and n are the orders with respect to A and B. Substituting the values from Experiment 1, \(3.35 × 10^{-4}\) MS^-1 = \(k(0.185)^1(0.133)^2\). Solve this equation for k.

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Most popular questions from this chapter

The half-lives of both zero-order and second-order reactions depend on the initial concentration, as well as on the rate constant. In one case, the half- life gets longer as the initial concentration increases, and in the other it gets shorter. Which is which, and why isn't the situation the same for both?

We have seen that the unit of \(k\) depends on the overall order of a reaction. Derive a general expression for the units of \(k\) for a reaction of any overall order, based on the order of the reaction (o) and the units of concentration (M) and time (s).

In three different experiments, the following results were obtained for the reaction \(A \longrightarrow\) products: \([\mathrm{A}]_{0}=1.00 \mathrm{M}, t_{1 / 2}=50 \mathrm{min} ;[\mathrm{A}]_{0}=200 \mathrm{M}, t_{1 / 2}=\) \(25 \min ;[\mathrm{A}]_{0}=0.50 \mathrm{M}, t_{1 / 2}=100 \mathrm{min} .\) Write the rate equation for this reaction, and indicate the value of \(k.\)

In the reaction \(A \longrightarrow\) products, at \(t=0\), the \([\mathrm{A}]=0.1565 \mathrm{M} .\) After \(1.00 \mathrm{min},[\mathrm{A}]=0.1498 \mathrm{M},\) and after \(2.00 \mathrm{min},[\mathrm{A}]=0.1433 \mathrm{M}\) (a) Calculate the average rate of the reaction during the first minute and during the second minute. (b) Why are these two rates not equal?

For the first-order reaction $$\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$ \(t_{1 / 2}=22.5 \mathrm{h}\) at \(20^{\circ} \mathrm{C}\) and \(1.5 \mathrm{h}\) at \(40^{\circ} \mathrm{C}.\) (a) Calculate the activation energy of this reaction. (b) If the Arrhenius constant \(A=2.05 \times 10^{13} \mathrm{s}^{-1}\) determine the value of \(k\) at \(30^{\circ} \mathrm{C}\).
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