Question

A mixture of one mole each of ${\mathrm{H}}_2$, $\mathrm{He}$ and ${\mathrm{O}}_2$each are enclosed in a cylinder of volume $V$ at temperature $T$. If the partial pressure of ${\mathrm{H}}_2$ is $2atm$, the total pressure of the gases in the cylinder is:

• A. $6atm$
• B. $14atm$
• C. $38atm$
• D. $22atm$

Answer 1

The correct option is A

$6atm$

Explanation for correct option:

(A) $\mathbf{6}\mathbf{}\mathit{a}\mathit{t}\mathit{m}$

1. The total pressure of the gases in the cylinder can be calculated by using Dalton's law of partial pressure.
2. According to Dalton's law of partial pressure $p_{\mathrm{i}}={\mathrm{x}}_{\mathrm{i}}\times {\mathrm{P}}_{\mathrm{t}}$ Where, $\mathrm{pi}$ is pressure of gas i in the mixture of gases, ${\mathrm{x}}_{\mathrm{i}}$ is mole fraction of gas i and ${\mathrm{P}}_{\mathrm{t}}$ is the total pressure of gases.
3. We know that the partial pressure of ${\mathrm{H}}_2$ gas in the mixture is $2atm$ and number of moles of each gas is $1\mathrm{mole}$.
4. Now, reforming the equation to use it we get: ${\mathrm{P}}_{\mathrm{t}}=\left(\frac{{\mathrm{n}}_{{\mathrm{H}}_2}+{\mathrm{n}}_{\mathrm{He}}+{\mathrm{n}}_{{\mathrm{o}}_2}}{{\mathrm{n}}_{{\mathrm{H}}_2}}\right)\times {\mathrm{p}}_{\mathrm{i}}$
5. Placing the known values in the equation: $$\begin{gathered} {\mathrm{P}}_{\mathrm{t}}=\left(\frac{3}{1}\times 2\right) \\ {\mathrm{P}}_{\mathrm{t}}=6 \end{gathered}$$
6. So, here we can see that total pressure of the gases is $6atm$.

Explanation for incorrect options:

(B) $\mathbf{14}\mathbf{}\mathit{a}\mathit{t}\mathit{m}$

1. According to Dalton's law of partial pressure the total pressure of gases is calculated above.
2. So option B is incorrect.

(C) $\mathbf{38}\mathbf{}\mathit{a}\mathit{t}\mathit{m}$

1. According to Dalton's law of partial pressure the total pressure of gases is calculated above.
2. So option C is incorrect.

(D) $\mathbf{22}\mathbf{}\mathit{a}\mathit{t}\mathit{m}$

1. According to Dalton's law of partial pressure the total pressure of gases is calculated above.
2. So option D is incorrect.

Hence option A is correct, the total pressure of the gases in the cylinder is $6atm$.