---
title: "A chemist studies the vapor-phase formation of a hypothetical coating precursor according to the overall reaction  \\[ \\text{AX(g)}+\\text{B(g)}+\\text{X(g)}\\rightarrow\\text{ABX}_2\\text{(g)} \\]  Initial-rate measurements at constant temperature give the following rate law.  \\[ \\text{rate}=k_{\\mathrm{obs}}\\dfrac{[\\text{AX}][\\text{B}]}{[\\text{X}]} \\]  The chemist proposes the mechanism below. Each step is elementary, and step \\(1\\) rapidly reaches equilibrium before the slow step occurs.  | Step | Proposed elementary process | |——|—————————–| | \\(1\\) | \\(\\text{AX(g)}\\rightleftharpoons\\text{A(g)}+\\text{X(g)}\\), fast equilibrium, \\(K_c=\\dfrac{k_1}{k_{-1}}\\) | | \\(2\\) | \\(\\text{A(g)}+\\text{B(g)}\\rightarrow\\text{AB(g)}\\), slow | | \\(3\\) | \\(\\text{AB(g)}+\\text{X(g)}\\rightarrow\\text{ABX(g)}\\), fast | | \\(4\\) | \\(\\text{ABX(g)}+\\text{X(g)}\\rightarrow\\text{ABX}_2\\text{(g)}\\), fast |  Which of the following correctly evaluates whether the proposed mechanism is consistent with both the overall reaction and the observed rate law?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120073/"
date_modified: "2026-08-21T08:41:12+00:00"
---

# A chemist studies the vapor-phase formation of a hypothetical coating precursor according to the overall reaction

\[
\text{AX(g)}+\text{B(g)}+\text{X(g)}\rightarrow\text{ABX}_2\text{(g)}
\]

Initial-rate measurements at constant temperature give the following rate law.

\[
\text{rate}=k_{\mathrm{obs}}\dfrac{[\text{AX}][\text{B}]}{[\text{X}]}
\]

The chemist proposes the mechanism below. Each step is elementary, and step \(1\) rapidly reaches equilibrium before the slow step occurs.

| Step | Proposed elementary process |
|——|—————————–|
| \(1\) | \(\text{AX(g)}\rightleftharpoons\text{A(g)}+\text{X(g)}\), fast equilibrium, \(K_c=\dfrac{k_1}{k_{-1}}\) |
| \(2\) | \(\text{A(g)}+\text{B(g)}\rightarrow\text{AB(g)}\), slow |
| \(3\) | \(\text{AB(g)}+\text{X(g)}\rightarrow\text{ABX(g)}\), fast |
| \(4\) | \(\text{ABX(g)}+\text{X(g)}\rightarrow\text{ABX}_2\text{(g)}\), fast |

Which of the following correctly evaluates whether the proposed mechanism is consistent with both the overall reaction and the observed rate law?

A chemist studies the vapor-phase formation of a hypothetical coating precursor according to the overall reaction

\[
\text{AX(g)}+\text{B(g)}+\text{X(g)}\rightarrow\text{ABX}_2\text{(g)}
\]

Initial-rate measurements at constant temperature give the following rate law.

\[
\text{rate}=k_{\mathrm{obs}}\dfrac{[\text{AX}][\text{B}]}{[\text{X}]}
\]

The chemist proposes the mechanism below. Each step is elementary, and step \(1\) rapidly reaches equilibrium before the slow step occurs.

| Step | Proposed elementary process |
|------|-----------------------------|
| \(1\) | \(\text{AX(g)}\rightleftharpoons\text{A(g)}+\text{X(g)}\), fast equilibrium, \(K_c=\dfrac{k_1}{k_{-1}}\) |
| \(2\) | \(\text{A(g)}+\text{B(g)}\rightarrow\text{AB(g)}\), slow |
| \(3\) | \(\text{AB(g)}+\text{X(g)}\rightarrow\text{ABX(g)}\), fast |
| \(4\) | \(\text{ABX(g)}+\text{X(g)}\rightarrow\text{ABX}_2\text{(g)}\), fast |

Which of the following correctly evaluates whether the proposed mechanism is consistent with both the overall reaction and the observed rate law?

- **A.** The mechanism is consistent, because its steps sum to the observed reaction and \(\text{X}\) is consumed only after the slow step, so increasing \([\text{X}]\) must decrease the overall rate.
- **B.** The mechanism is consistent, because its steps sum to the observed reaction and the fast equilibrium gives \([\text{A}]=K_c[\text{AX}]/[\text{X}]\), which converts the slow-step rate law into the observed rate law.
- **C.** The mechanism is not consistent, because even though its steps sum to the observed reaction, the concentration of a net reactant such as \(\text{X}\) cannot have a negative exponent in a rate law.
- **D.** The mechanism is not consistent, because the fast equilibrium gives \([\text{A}]=[\text{X}]/(K_c[\text{AX}])\), which produces a positive dependence on \([\text{X}]\) in the slow-step rate law.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120073/*