In this chapter we learned that a catalyst has no effect on the position of an equilibrium because it speeds up both the forward and reverse rates to the same extent. To test this statement, consider a situation in which an equilibrium of the type $$ 2 \mathrm{~A}(g) \rightleftharpoons \mathrm{B}(g) $$ is established inside a cylinder fitted with a weightless piston. The piston is attached by a string to the cover of a box containing a catalyst. When the piston moves upward (expanding against atmospheric pressure), the cover is lifted and the catalyst is exposed to the gases. When the piston moves downward, the box is closed. Assume that the catalyst speeds up the forward reaction \((2 \mathrm{~A} \longrightarrow \mathrm{B})\) but does not affect the reverse process \((\mathrm{B} \longrightarrow 2 \mathrm{~A})\). Suppose the catalyst is suddenly exposed to the equilibrium system as shown below. Describe what would happen subsequently. How does this "thought" experiment convince you that no such catalyst can exist?

Step by step solution

01

Understand the Reaction

The given reaction is \(2A \rightleftharpoons B\). This means that two moles of gas A are in equilibrium with one mole of gas B. Both forward and reverse reactions are possible.

02

Understand the Role of Catalyst

In general, a catalyst speeds up both forward and reverse reactions equally, having no effect on the equilibrium of the system. But the catalyst in the problem is said to only speed up the forward reaction, i.e., converting A to B and does not affect the reverse reaction (B to 2A).

03

Analyze the Effect of Catalyst

When the catalyst is exposed to the gases, it will speed up the conversion of A to B. Because the reverse reaction is not equally accelerated, there will be more B produced than A since the forward reaction is favored. This will result in the piston rising as the gas volume decreases (from two moles of A to one mole of B). This continues until the catalyst is covered again.

04

Explain Why the Described Catalyst Cannot Exist

If the catalyst acted as described in the problem, it would violate the principle of chemical equilibrium, which states that at equilibrium, the rate of forward reaction equals the rate of reverse reaction. The given catalyst would only speed up the forward reaction, disrupting the equilibrium. Therefore, such a catalyst cannot exist.

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