A mixture of one mole each of
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 $\mathrm{T}$. If the partial pressure of $\mathrm{H}_{2}$ is $2 \mathrm{~atm}$, the total pressure of the gases in the cylinder is :

 

  1. $14 \mathrm{~atm}$

  2. $22 \mathrm{~atm}$

  3. $6 \mathrm{~atm}$

  4. 38 atm


Correct Option: , 3

Solution:

According to Dalton’s law of partial pressure

$\mathrm{p}_{\mathrm{i}}=\mathrm{x}_{\mathrm{i}} \times \mathrm{P}_{\mathrm{T}}$

$\mathrm{p}_{\mathrm{i}}=$ partial pressure of the $\mathrm{i}^{\text {th }}$ component

$\mathrm{x}_{\mathrm{i}}=$ mole fraction of the $\mathrm{i}^{\text {th }}$ component

$\mathrm{p}_{\mathrm{T}}=$ total pressure of mixture

$\Rightarrow 2 \mathrm{~atm}=\left(\frac{\mathrm{n}_{\mathrm{H}_{2}}}{\mathrm{n}_{\mathrm{H}_{2}}+\mathrm{n}_{\mathrm{H}_{\mathrm{e}}}+\mathrm{n}_{\mathrm{O}_{2}}}\right) \times \mathrm{p}_{\mathrm{T}}$

$\Rightarrow \mathrm{p}_{\mathrm{T}}=2 \mathrm{~atm} \times \frac{3}{1}=6 \mathrm{~atm}$

 

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