Question

What ratio by mass of 'Ne' and \(\text{CH}_4\) should be mixed so that partial pressure exerted by each gas is same?

• A. \(1:1\)
• B. \(2:1\)
• C. \(2:3\)
• D. \(5:4\)

Hint:

At the same T and V, equal partial pressure means equal number of moles.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In a mixture of gases in one container, partial pressure is \(p_i = x_i P_{total}\), which depends on mole fraction. Equal partial pressures need equal mole fractions, so the two gases must have equal moles.

Step 2: Key Formula or Approach:
For \(n\) moles, mass \(= n \times M\). Molar masses: Ne \(= 20\) g/mol, \(\text{CH}_4 = 16\) g/mol.

Step 3: Detailed Explanation:
Let each gas be \(1\) mole.
Mass of Ne \(= 20\) g and mass of \(\text{CH}_4 = 16\) g.
\[ \frac{m_{\text{Ne}}}{m_{\text{CH}_4}} = \frac{20}{16} = \frac{5}{4} \]
A \(1:1\) mass ratio would give more moles of the lighter methane, so its partial pressure would be larger. The ratios \(2:1\) and \(2:3\) do not give equal moles either.

Final Answer:
The mass ratio of Ne to \(\text{CH}_4\) is \(5:4\), option (D). \[ \boxed{5:4} \]