Thallium(I) is oxidized by cerium(IV) as follows: $$ \mathrm{Tl}^{+}+2 \mathrm{Ce}^{4+} \longrightarrow \mathrm{Tl}^{3+}+2 \mathrm{Ce}^{3+} $$ The elementary steps, in the presence of \(\mathrm{Mn}(\mathrm{II}),\) are as follows: $$ \begin{aligned} \mathrm{Ce}^{4+}+\mathrm{Mn}^{2+} & \longrightarrow \mathrm{Ce}^{3+}+\mathrm{Mn}^{3+} \\ \mathrm{Ce}^{4+}+\mathrm{Mn}^{3+} \longrightarrow \mathrm{Ce}^{3+}+\mathrm{Mn}^{4+} \\ \mathrm{Tl}^{+}+\mathrm{Mn}^{4+} \longrightarrow \mathrm{Tl}^{3+}+\mathrm{Mn}^{2+} \end{aligned} $$ (a) Identify the catalyst, intermediates, and the ratedetermining step if the rate law is given by rate \(=\) \(k\left[\mathrm{Ce}^{4+}\right]\left[\mathrm{Mn}^{2+}\right]\) (b) Explain why the reaction is slow without the catalyst. (c) Classify the type of catalysis (homogeneous or heterogeneous).

Step by step solution

01

Identifying the catalyst and intermediates

Catalysts are substances that increase the rate of a reaction but remain unchanged by the end of the reaction. Intermediates, however, are formed during the reaction but get consumed by the end of the reaction. The easiest way to identify the catalyst and intermediates is by comparing the reactants and products in the overall reaction with the substances involved in the elementary steps. After comparison, it's noticed that \(\mathrm{Mn}^{2+}\) appears in the overall reaction equation and the elementary steps, unchanged, hence it is the catalyst, while \(\mathrm{Mn}^{3+}\) and \(\mathrm{Mn}^{4+}\) appear in the elementary steps but not in the overall reaction, hence, they're intermediates

02

Identifying the rate-determining step

The rate-determining step of a reaction is the slowest step, and hence it determines the rate of the reaction. The rate law of the reaction is given by rate= \(k\left[\mathrm{Ce}^{4+}\right]\left[\mathrm{Mn}^{2+}\right]\). Looking at each of the elementary steps, the one that fits the rate law is: \(\mathrm{Ce}^{4+}+\mathrm{Mn}^{2+}\) leading to \(\mathrm{Ce}^{3+}+\mathrm{Mn}^{3+}\). Therefore, this is the rate-determining step.

03

Explaining why the reaction is slow without the catalyst

The use of catalysts helps to provide an alternative pathway with a lower activation energy for the reaction. Thus, without the catalyst, the reaction has to follow the primary path, which has a higher activation energy and hence is slower.

04

Classifying the type of catalysis

There are two types of catalysis: Homogeneous catalysis where the catalyst and the reactants are in the same phase, and heterogeneous catalysis where the catalyst and the reactants are in different phases. In the given reaction, since both the catalyst and the reactants are in the aqueous phase, it is a homogeneous catalysis type.

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