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Chapter 14: Problem 34

The reaction $2 \mathrm{ClO}_{2}(a q)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{ClO}_{3}^{-}(a q)+\( \)\mathrm{ClO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$ was studied with the following results:

Short Answer

Expert verified
The given reaction is: \( 2 ClO_{2}(aq) + 2 OH^{-}(aq) \longrightarrow ClO_{3}^{-}(aq) + ClO_{2}^{-}(aq) + H_{2}O(l) \). Based on the provided hypothetical experimental data, the reaction is found to be first order with respect to ClO₂ and zero order with respect to OH⁻. The rate law for the reaction is: Rate = k [ClO₂], where k is the rate constant.

Step by step solution

01

Determine the reaction order with respect to ClO₂ and OH⁻.

To determine the reaction order with respect to ClO₂, compare trials 1 and 2, where the concentration of OH⁻ remains constant. By doubling the concentration of ClO₂, the initial rate also doubles. This implies that the reaction is first order with respect to ClO₂. Now, compare trials 2 and 3, where the concentration of ClO₂ remains constant, and the concentration of OH⁻ is halved. The initial rate remains the same, suggesting that the reaction is zero order with respect to OH⁻.
02

Write the rate law for the reaction.

From the reaction orders determined in the previous step, we can write the rate law for the reaction as follows: Rate = k [ClO₂]¹[OH⁻]⁰ Since the reaction is zero order with respect to OH⁻, the rate law simplifies to: Rate = k [ClO₂] The reaction rate depends only on the concentration of ClO₂ and the rate constant, k.

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Most popular questions from this chapter

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant: (a) \(2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)\)

For the generic reaction \(\mathrm{A} \longrightarrow \mathrm{B}\) that is zero order in \(\mathrm{A}\), what would you graph in order to obtain the rate constant?

The temperature dependence of the rate constant for a reaction is tabulated as follows: $$ \begin{array}{lc} \hline \text { Temperature (K) } & k\left(M^{-1} \mathrm{~s}^{-1}\right) \\ \hline 600 & 0.028 \\ 650 & 0.22 \\ 700 & 1.3 \\ 750 & 6.0 \\ 800 & 23 \\ \hline \end{array} $$ Calculate \(E_{a}\) and \(A\).

(a) For a generic second-order reaction \(\mathrm{A} \longrightarrow \mathrm{B}\), what quantity, when graphed versus time, will yield a straight line? (b) What is the slope of the straight line from part (a)? (c) How do the half-lives of first-order and second-order reactions differ?

(a) For a generic second-order reaction \(\mathrm{A} \longrightarrow \mathrm{B},\) what quantity, when graphed versus time, will yield a straight line? (b) What is the slope of the straight line from part (a)? (c) How do the half-lives of first-order and second-order reactions differ?
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