---
title: "A student compares three possible pathways for the same reaction at the same temperature. Pathway U is uncatalyzed, whereas pathways P and Q use different catalysts. The potential-energy profiles are shown. For this comparison, the frequency factor, \\(A\\), in the Arrhenius equation is the same for all three pathways. The corresponding forward rate constants are \\(k_U\\), \\(k_P\\), and \\(k_Q\\).  Which ranking of the forward rate constants is correct, and which statement best explains the ranking?"
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url: "https://nerd-notes.com/ubq/119502/"
date_modified: "2026-08-19T12:40:51+00:00"
---

# A student compares three possible pathways for the same reaction at the same temperature. Pathway U is uncatalyzed, whereas pathways P and Q use different catalysts. The potential-energy profiles are shown. For this comparison, the frequency factor, \(A\), in the Arrhenius equation is the same for all three pathways. The corresponding forward rate constants are \(k_U\), \(k_P\), and \(k_Q\).

Which ranking of the forward rate constants is correct, and which statement best explains the ranking?

A student compares three possible pathways for the same reaction at the same temperature. Pathway U is uncatalyzed, whereas pathways P and Q use different catalysts. The potential-energy profiles are shown. For this comparison, the frequency factor, \(A\), in the Arrhenius equation is the same for all three pathways. The corresponding forward rate constants are \(k_U\), \(k_P\), and \(k_Q\).

Which ranking of the forward rate constants is correct, and which statement best explains the ranking?

![Draw a grayscale potential-energy diagram with bare axes and no gridlines. The vertical axis is labeled “Potential energy,” increasing upward, and the horizontal axis is labeled “Reaction progress,” increasing to the right. A legend maps the solid curve to U (uncatalyzed), the dashed curve to P (catalyst P), and the dotted curve to Q (catalyst Q). All three curves begin at one common reactant-energy level near the left edge and end at one common, lower product-energy level near the right edge. The solid curve rises to the highest single maximum at about the horizontal midpoint. The dashed curve rises to an intermediate-height single maximum about one-third across. The dotted curve rises to the lowest single maximum about three-quarters across. Each curve descends smoothly to the shared product level. No numerical ticks, gridlines, arrows, other labels, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787143250-2JKiyF.jpg)

- **A.** \(k_U>k_P>k_Q\), because a larger \(E_a\) results in a larger rate constant.
- **B.** \(k_P>k_U>k_Q\), because an earlier transition state along the reaction coordinate results in a larger rate constant.
- **C.** \(k_P>k_Q>k_U\), because both catalysts lower \(E_a\), and pathway P has the smaller activation-energy barrier.
- **D.** \(k_Q>k_P>k_U\), because a smaller \(E_a\) increases the fraction of collisions having sufficient energy to react.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119502/*