A closed vessel contains 10 g of an ideal gas X at 300 K , which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm . The ratio of root mean square velocities of X and Y at 300 K is

Chemistry · States of Matter - Gaseous State

JEE Advanced 2024 — Paper 1 — Question 34

A closed vessel contains 10 g of an ideal gas $\mathbf{X}$ at 300 K , which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas $\mathbf{Y}$ is added to it and the pressure becomes 6 atm . The ratio of root mean square velocities of $X$ and $Y$ at 300 K is

Option A:
$2 \sqrt{2}: \sqrt{3}$
Option B:
$2 \sqrt{2}: 1$
Option C:
$1: 2$
Option D:
$2: 1$
Correct

Answer: D

Step-by-step solution

$2 \times V=\frac{10}{M_{x}} \times R \times T$

\begin{gathered} 4 \times \mathrm{V}=\frac{80}{\mathrm{M}_{\mathrm{y}}} \times \mathrm{R} \times \mathrm{T} \end{gathered}

\begin{gathered} 2=\frac{80 \times M_{x}}{M_{y} \times 10} \end{gathered}

$\frac{M_{x}}{M_{y}}=\frac{1}{4}$

$\frac{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{x}{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{y}}\}=\sqrt{\frac{4}{1}}=\frac{2}{1}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2024
Paper: Paper 1
Subject: Chemistry
Chapter: States of Matter - Gaseous State
Topic: KTG + Velocities of Gas Molecules