Question

Hydroxide ion is involved in the mechanism of the following reaction but is not consumed in the overall reaction. $$\mathrm{OCI}^{-}+\mathrm{I}^{-} \stackrel{\mathrm{OH}^{-}}{\longrightarrow} \mathrm{OI}^{-}+\mathrm{Cl}^{-}$$ (a) From the data given, determine the order of the reaction with respect to \(\mathrm{OCl}^{-}, \mathrm{I}^{-},\) and \(\mathrm{OH}^{-}\) (b) What is the overall reaction order? (c) Write the rate equation, and determine the value of the rate constant, \(k.\) $$\begin{array}{lccl} \hline & & & \text { Rate Formation } \\ {\left[\mathrm{OC}^{-}\right], \mathrm{M}} & {\left[\mathrm{l}^{-}\right], \mathrm{M}} & {\left[\mathrm{OH}^{-}\right], \mathrm{M}} & \mathrm{O}^{-}, \mathrm{M} \mathrm{s}^{-1} \\ \hline 0.0040 & 0.0020 & 1.00 & 4.8 \times 10^{-4} \\ 0.0020 & 0.0040 & 1.00 & 5.0 \times 10^{-4} \\ 0.0020 & 0.0020 & 1.00 & 2.4 \times 10^{-4} \\ 0.0020 & 0.0020 & 0.50 & 4.6 \times 10^{-4} \\ 0.0020 & 0.0020 & 0.25 & 9.4 \times 10^{-4} \\ \hline \end{array}$$

Short answer

The orders of reaction are: \(OCl^-\): first order, \(I^-\): zero order, \(OH^-\): zero order. The overall order of reaction is 1. The rate equation is: Rate = k * [\(OCl^-\)], and the rate constant, k, is 0.12 s^−1.

Step-by-step solution

Determining Reaction Order with Respect to Each Reactant

The reaction order with respect to each reactant can be determined by observing how the rate changes with changes in the concentration of each reactant. From the data:a) The concentration of \(OCl^-\) is halved from 0.0040 M to 0.0020 M, the concentration of \(I^-\) and \(OH^-\) remain constant, and the rate of reaction is also halved. This indicates the reaction is first-order with respect to \(OCl^-\).b) The concentration of \(I^-\) is doubled from 0.0020 M to 0.0040 M, the concentration of \(OCl^-\) and \(OH^-\) remained constant, and the rate remains constant. This implies the reaction is zero-order with respect to \(I^-\).c) When the concentration of \(OH^-\) is reduced by half from 1.00M to 0.50M, while keeping the concentrations of the other reactants constant, the rate does not change. This means the reaction is zero-order with respect to \(OH^-\).

Determining Overall Reaction Order

The overall order of reaction is the sum of the orders of reaction with respect to each reactant, which in this case is 1 (from \(OCl^-\)) + 0 (from \(I^-\)) + 0 (from \(OH^-\)) = 1. So, the overall order of reaction is 1.

Writing Rate Equations and Determining Rate Constant

The rate equation considering each order of reaction is: Rate = k * [\(OCl^-\)] . With Rate = \(4.8 × 10^{-4}\) and [\(OCl^-\)] = 0.0040, solving for rate constant 'k' we get: k = Rate/[\(OCl^-\)] = \(4.8 \times 10^{-4}\) M/s / 0.0040 M = 0.12 s^−1

Key concepts

Chemical Kinetics

Chemical kinetics is the study of the rates at which chemical reactions proceed and the factors affecting those rates. It's crucial for understanding reaction mechanisms, which describe the step-by-step process by which reactants transform into products. One basic component of kinetics is the reaction order, which tells us how the rate is affected by the concentration of reactants. This is established experimentally by observing changes in the concentrations of reactants over time and the corresponding changes in reaction rate.

For instance, when the concentration of \(\mathrm{OCl}^{-}\) in our exercise is reduced, the rate diminishes by the same proportion, suggesting a direct relationship, indicative of a first-order reaction with respect to \(\mathrm{OCl}^{-}\). In contrast, altering \(\mathrm{I}^{-}\) and \(\mathrm{OH}^{-}\) concentrations does not change the rate, which suggests they both have a zero-order dependence. Comprehending these dependencies is essential as it allows the prediction of how a change in one reactant concentration would impact the reaction rate, essential for the controlled execution of chemical processes.

Rate Equation

The rate equation, or rate law, expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is determined empirically and reflects the reaction order with respect to each reactant. In our exercise, the experimentally determined reaction orders are used to construct the rate equation. For a general reaction where \(A\) and \(B\) are reactants, the rate equation could look like \( Rate = k[\mathrm{A}]^{m}[\mathrm{B}]^{n} \), where \(m\) and \(n\) are the reaction orders with respect to \(A\) and \(B\), respectively. The rate constant, \(k\), is a proportionality constant that offers insight into the reaction rate under specific conditions.

In the case of the \(\mathrm{OCl}^{-}\) and \(\mathrm{I}^{-}\) reaction, since \(\mathrm{I}^{-}\) and \(\mathrm{OH}^{-}\) have no effect on the rate, their reaction order is zero and they do not appear in the rate equation. Hence, the rate equation simplifies to \( Rate = k[\mathrm{OCl}^{-}] \), where the reaction is first-order with respect to \(\mathrm{OCl}^{-}\). Understanding how to formulate and use this equation is pivotal for predicting how fast a reaction will occur under varying conditions.

Rate Constant

The rate constant is a key aspect of the rate equation that provides insight into the speed of a reaction at a given temperature, under a certain set of conditions. It is independent of reactant concentrations but varies with temperature and the presence of a catalyst. In mathematical terms, the rate constant bridges the gap between the concentration of reactants and the rate of reaction.

For a reaction that is first-order with respect to a single reactant, like our \(\mathrm{OCl}^{-}\) and \(\mathrm{I}^{-}\) example, the larger the value of the rate constant, the faster the reaction proceeds. By evaluating experimental data, we use the rate equation to solve for the rate constant \(k\) as it relates to the known concentration of the reactants and the measured initial rate. In this exercise, the calculated rate constant is \(k = 0.12 \, \mathrm{s}^{-1}\), which signifies the speed at which \(\mathrm{OCl}^{-}\) reacts under the given conditions. Knowing the rate constant is crucial for designing and controlling chemical processes, such as synthesis, where precise timing and reaction control are imperative.