Question

A vessel of volume \(20\,\text{L}\) contains a mixture of hydrogen and helium at temperature \(27^\circ\text{C}\) and pressure \(2\,\text{atm}\). The mass of the mixture is \(5\,\text{g}\). Assuming the gases to be ideal, the ratio of mass of hydrogen to that of helium in the mixture is:

• A. \(1:2\)
• B. \(2:3\)
• C. \(2:1\)
• D. \(2:5\)

Hint:

For gas mixtures: \[ n=\sum \frac{m}{M} \] Use molecular masses carefully.

Answer 1

The Correct Option is C

Step 1: Total moles: \[ n=\frac{PV}{RT} \]
Step 2: Let masses be \(m_1\) (H\(_2\)) and \(m_2\) (He): \[ \frac{m_1}{2} + \frac{m_2}{4} = n \]
Step 3: Given: \[ m_1+m_2=5 \]
Step 4: Solving gives: \[ m_1:m_2 = 2:1 \]