---
title: "The distribution of molecular speeds for a sample of \\(1.0 \\text{ mol}\\) of \\(\\text{N}_2(g)\\) in a rigid container at two different temperatures, \\(T_1\\) and \\(T_2\\), is shown in the graph below.  Which of the following correctly compares \\(T_1\\) and \\(T_2\\) and provides the correct justification based on the root-mean-square speed (\\(v_{\\text{rms}}\\)) of the gas molecules?"
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url: "https://nerd-notes.com/ubq/121442/"
date_modified: "2026-08-23T05:02:31+00:00"
---

# The distribution of molecular speeds for a sample of \(1.0 \text{ mol}\) of \(\text{N}_2(g)\) in a rigid container at two different temperatures, \(T_1\) and \(T_2\), is shown in the graph below.

Which of the following correctly compares \(T_1\) and \(T_2\) and provides the correct justification based on the root-mean-square speed (\(v_{\text{rms}}\)) of the gas molecules?

The distribution of molecular speeds for a sample of \(1.0 \text{ mol}\) of \(\text{N}_2(g)\) in a rigid container at two different temperatures, \(T_1\) and \(T_2\), is shown in the graph below.

Which of the following correctly compares \(T_1\) and \(T_2\) and provides the correct justification based on the root-mean-square speed (\(v_{\text{rms}}\)) of the gas molecules?

![A 2D line graph plotted on bare axes with no gridlines. The horizontal axis is labeled 'Molecular speed' and the vertical axis is labeled 'Relative number of molecules'. Two curves originate at the origin (0,0). The first curve is drawn with a solid line and is labeled '\(T_1\)'; it rises sharply to a tall peak at a lower speed value and drops quickly, tailing off near the middle of the speed axis. The second curve is drawn with a dashed line and is labeled '\(T_2\)'; it rises more gradually to a shorter, broader peak shifted significantly to the right of the first peak and extends with a longer tail toward higher speed values. The area under both curves is equal. No other curves, gridlines, labels, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461350-zdAUsW.jpg)

- **A.** \(T_2 > T_1\), because the distribution for \(T_2\) is shifted toward higher speeds, corresponding to a greater average kinetic energy and a higher \(v_{\text{rms}}\).
- **B.** \(T_2 > T_1\), because the lower peak height for \(T_2\) indicates that fewer molecules are in motion, resulting in a higher \(v_{\text{rms}}\).
- **C.** \(T_1 > T_2\), because the higher peak height for \(T_1\) indicates that a greater fraction of molecules possess high kinetic energy and a higher \(v_{\text{rms}}\).
- **D.** \(T_1 > T_2\), because the narrower distribution for \(T_1\) indicates that the gas molecules have a higher average kinetic energy and a higher \(v_{\text{rms}}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121442/*