A 10 g mixture of hydrogen and helium is contained in a vessel of capacity $0.0125 \mathrm{~m}^{3}$ at 6 bar and $27^{\circ} \mathrm{C}$. The mass of helium in the mixture is \_\_\_\_ g. (nearest integer) Given : $\mathrm{R}=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ (Atomic masses of H and He are 1 u and 4 u , respectively)

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Some Basic Concepts of Chemistry

A 10 g mixture of hydrogen and helium is contained in a vessel of capacity

0.0125 m^{3}

at 6 bar and

2 7^{\circ} C

. The mass of helium in the mixture is
____ g. (nearest integer)

Given :

R = 8.3 JK^{- 1} mol^{- 1}

(Atomic masses of H and He are 1 u and 4 u , respectively)

Answer: 8

Using the ideal gas equation

P V = n_{mix} R T

n_{mix} = \frac{P V}{R T} = \frac{6 \times 1 0 ^{5} \times 0.0125}{8.3 \times 300} = 3

mol

Let moles of He =

x

and moles of

H_{2}

(3 - x)

Total mass:

4 x + 2 (3 - x) = 10

Solving:

4 x + 6 - 2 x = 10 \Rightarrow 2 x = 4 \Rightarrow x = 2

mol

Mass of He =

2 \times 4 = 8

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Integer answer