Which of the following statement(s) is(are) correct regarding the root mean square speed ( U rms ) and average translational kinetic energy ( varepsilon av ) of a molecule in a gas at equilibrium?

varepsilon av at a given temperature does not depend on its molecular mass

U rms is doubled when its temperature is increased four times

U rms is inversely proportional to the square root of its molecular mass

varepsilon av is doubled when its temperature is increased four times

Chemistry · States of Matter - Gaseous State

JEE Advanced 2019 — Paper 1 — Question 23

Which of the following statement(s) is(are) correct regarding the root mean square speed ( $\mathrm{U}_{\mathrm{rms}}$ ) and average translational kinetic energy ( $\varepsilon_{\mathrm{av}}$ ) of a molecule in a gas at equilibrium?

Option A:
$\varepsilon_{\mathrm{av}}$ at a given temperature does not depend on its molecular mass
Correct
Option B:
$\mathrm{U}_{\mathrm{rms}}$ is doubled when its temperature is increased four times
Correct
Option C:
$\varepsilon_{\mathrm{av}}$ is doubled when its temperature is increased four times
Option D:
$\mathrm{U}_{\mathrm{rms}}$ is inversely proportional to the square root of its molecular mass
Correct

Answer: A, B, D

Step-by-step solution

$\mathrm{E}_{\mathrm{av}}=\frac{3}{2} \mathrm{RT} \quad \mathrm{U}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$

$\mathrm{E}_{\mathrm{av}}$ does not depend on its molecular mass but depends upon absolute temperature.

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2019
Paper: Paper 1
Subject: Chemistry
Chapter: States of Matter - Gaseous State
Topic: KTG + Velocities of Gas Molecules