---
title: "A student investigates the reversible reaction  \\[ \\text{A(aq)} \\rightleftharpoons \\text{B(aq)} \\]  at \\(298\\ \\text{K}\\). The student assigns each catalyzed pathway one of the following labels: homogeneous nonenzymatic, heterogeneous, or enzymatic. The observations and measured activation energies are shown below.  | Pathway | Observation | \\(E_{a,\\mathrm{f}}\\) \\((\\text{kJ mol}^{-1})\\) | \\(E_{a,\\mathrm{r}}\\) \\((\\text{kJ mol}^{-1})\\) | |—|—|—:|—:| | \\(\\text{U}\\) | No catalyst is present. | \\(80\\) | \\(50\\) | | \\(\\text{P}\\) | \\(\\text{C(aq)}\\) forms \\(\\text{AC(aq)}\\) in an elementary step and is regenerated in a later step. | \\(55\\) | \\(25\\) | | \\(\\text{Q}\\) | \\(\\text{A(aq)}\\) adsorbs onto \\(\\text{M(s)}\\), reacts on its surface, and desorbs as \\(\\text{B(aq)}\\). | \\(45\\) | \\(15\\) | | \\(\\text{R}\\) | A dissolved protein \\(\\text{E(aq)}\\) binds \\(\\text{A(aq)}\\) at a shape-specific active site, releases \\(\\text{B(aq)}\\), and is regenerated. | \\(40\\) | \\(10\\) |  Which statement correctly classifies pathways \\(\\text{P}\\), \\(\\text{Q}\\), and \\(\\text{R}\\) and predicts how each catalyst affects the equilibrium ratio \\(\\dfrac{[\\text{B}]}{[\\text{A}]}\\) relative to pathway \\(\\text{U}\\)?"
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url: "https://nerd-notes.com/ubq/120087/"
date_modified: "2026-08-21T08:41:23+00:00"
---

# A student investigates the reversible reaction

\[
\text{A(aq)} \rightleftharpoons \text{B(aq)}
\]

at \(298\ \text{K}\). The student assigns each catalyzed pathway one of the following labels: homogeneous nonenzymatic, heterogeneous, or enzymatic. The observations and measured activation energies are shown below.

| Pathway | Observation | \(E_{a,\mathrm{f}}\) \((\text{kJ mol}^{-1})\) | \(E_{a,\mathrm{r}}\) \((\text{kJ mol}^{-1})\) |
|—|—|—:|—:|
| \(\text{U}\) | No catalyst is present. | \(80\) | \(50\) |
| \(\text{P}\) | \(\text{C(aq)}\) forms \(\text{AC(aq)}\) in an elementary step and is regenerated in a later step. | \(55\) | \(25\) |
| \(\text{Q}\) | \(\text{A(aq)}\) adsorbs onto \(\text{M(s)}\), reacts on its surface, and desorbs as \(\text{B(aq)}\). | \(45\) | \(15\) |
| \(\text{R}\) | A dissolved protein \(\text{E(aq)}\) binds \(\text{A(aq)}\) at a shape-specific active site, releases \(\text{B(aq)}\), and is regenerated. | \(40\) | \(10\) |

Which statement correctly classifies pathways \(\text{P}\), \(\text{Q}\), and \(\text{R}\) and predicts how each catalyst affects the equilibrium ratio \(\dfrac{[\text{B}]}{[\text{A}]}\) relative to pathway \(\text{U}\)?

A student investigates the reversible reaction

\[
\text{A(aq)} \rightleftharpoons \text{B(aq)}
\]

at \(298\ \text{K}\). The student assigns each catalyzed pathway one of the following labels: homogeneous nonenzymatic, heterogeneous, or enzymatic. The observations and measured activation energies are shown below.

| Pathway | Observation | \(E_{a,\mathrm{f}}\) \((\text{kJ mol}^{-1})\) | \(E_{a,\mathrm{r}}\) \((\text{kJ mol}^{-1})\) |
|---|---|---:|---:|
| \(\text{U}\) | No catalyst is present. | \(80\) | \(50\) |
| \(\text{P}\) | \(\text{C(aq)}\) forms \(\text{AC(aq)}\) in an elementary step and is regenerated in a later step. | \(55\) | \(25\) |
| \(\text{Q}\) | \(\text{A(aq)}\) adsorbs onto \(\text{M(s)}\), reacts on its surface, and desorbs as \(\text{B(aq)}\). | \(45\) | \(15\) |
| \(\text{R}\) | A dissolved protein \(\text{E(aq)}\) binds \(\text{A(aq)}\) at a shape-specific active site, releases \(\text{B(aq)}\), and is regenerated. | \(40\) | \(10\) |

Which statement correctly classifies pathways \(\text{P}\), \(\text{Q}\), and \(\text{R}\) and predicts how each catalyst affects the equilibrium ratio \(\dfrac{[\text{B}]}{[\text{A}]}\) relative to pathway \(\text{U}\)?

- **A.** Pathways \(\text{P}\), \(\text{Q}\), and \(\text{R}\) are homogeneous nonenzymatic, heterogeneous, and enzymatic, respectively, and each catalyst increases \(\dfrac{[\text{B}]}{[\text{A}]}\) because lowering the forward activation energy favors formation of \(\text{B(aq)}\).
- **B.** Pathways \(\text{P}\), \(\text{Q}\), and \(\text{R}\) are homogeneous nonenzymatic, enzymatic, and heterogeneous, respectively, and each catalyst leaves \(\dfrac{[\text{B}]}{[\text{A}]}\) unchanged because it lowers the forward and reverse activation energies by the same amount.
- **C.** Pathways \(\text{P}\), \(\text{Q}\), and \(\text{R}\) are homogeneous nonenzymatic, heterogeneous, and enzymatic, respectively, and each catalyst leaves \(\dfrac{[\text{B}]}{[\text{A}]}\) unchanged because it provides an alternate pathway that lowers the forward and reverse activation energies without changing the relative energies of \(\text{A(aq)}\) and \(\text{B(aq)}\).
- **D.** Pathways \(\text{P}\), \(\text{Q}\), and \(\text{R}\) are homogeneous nonenzymatic, heterogeneous, and enzymatic, respectively, and each catalyst leaves \(\dfrac{[\text{B}]}{[\text{A}]}\) unchanged because the catalyst causes \(k_{\mathrm{f}}=k_{\mathrm{r}}\) when equilibrium is reached.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120087/*