Question

Equal weight of ${CH}_4$ and $H_2$ are mixed in a container at ${25}^{o}C$, the fraction of total pressure exerted by hydrogen is :

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{9}$
• D. $\frac{8}{9}$

Answer 1

The correct option is D $\frac{8}{9}$

Let the weight of methane and hydrogen added be x grams.

Then, moles of methane$=\frac{x}{16}$

And, moles of hydrogen$=\frac{x}{2}$

Now , we know that $PV=nRT$.(where P is pressure, n is the number of moles, V is the volume, T is the temperature, and R is the gas constant.)

In this case, V, R and T are constant. Hence,$P\propto n$$\Rightarrow P_{Total}=\frac{x}{16}+\frac{x}{2}=\frac{9}{16}x$ $\to \left(1\right)$

Also, $P_{Hydrogen}\propto \frac{x}{2}$ $\to \left(2\right)$

Now, dividing equation (2) by (1), we get fraction of total pressure exerted by hydrogen$=\frac{\frac{x}{2}}{\frac{9x}{16}}=\frac{8}{9}$, which is the required answer.