Question

Equal weights of ethane and hydrogen are mixed in an empty container at $25°\mathrm{C}$. The fraction of the total pressure exerted by hydrogen is:

• A. $1:2$
• B. $1:1$
• C. $1:16$
• D. $15:16$

Answer 1

The correct option is D

$15:16$

Explanation for correct option:

option (D) $15:16$

Step 1: Find Mole fraction of Hydrogen

The mole fraction is the number of moles of a specific component in the solution divided by the total number of moles in the given solution.

Let $\mathrm{x}\mathrm{g}$ each of Hydrogen and Ethane are mixed.

The moles of hydrogen and methane are $\frac{\mathrm{x}}{2}$ and $\frac{\mathrm{x}}{30}$ respectively as the mass of Hydrogen (${\mathrm{H}}_2$) and ethane (${\mathrm{C}}_2{\mathrm{H}}_6$) is $2\mathrm{g}{\mathrm{mol}}^{-1}$ and $30\mathrm{g}{\mathrm{mol}}^{-1}$ respectively.

The mole fraction of hydrogen is

$\frac{{\displaystyle \frac{\mathrm{x}}{2}}}{{\displaystyle \frac{\mathrm{x}}{2}}+{\displaystyle \frac{\mathrm{x}}{30}}}=\frac{15}{16}$

Step 2: Find fraction of the total pressure exerted by hydrogen

The partial pressure of each gas in a mixture is proportional to its mole fraction.

The partial pressure of Hydrogen is the product of its mole fraction and total pressure.

Thus $\frac{\mathrm{Partial}\mathrm{pressure}\mathrm{of}{\mathrm{H}}_2}{\mathrm{Total}\mathrm{pressure}}=\mathrm{mole}\mathrm{fraction}\mathrm{of}\mathrm{Hydrogen}=\frac{15}{16}$

So, option (d) is correct.