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Ideal Gas Equation from KTG

Equal mass of...

Question

Equal mass of $H_{2}$ , $H e$ and $C H_{4}$ are mixed in empty container at $300$ K, when total pressure is $2.6$ atm. The partial pressure of $H_{2}$ in the mixture is:

A

2.1

atm.

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B

1.6

atm.

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C

0.8

atm.

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D

0.2

atm.

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Solution

The correct option is B $1.6$ atm.
According to Dalton's law, the partial pressure of a gas is equals to the product of total pressure and mole fraction.
We have $H_{2}, H e a n d C H_{4}$ gas with equal mass, m.
Total Pressure = 2.6 atm
$P a r t i a l P r e s s u r e o f H_{2} = T o t a l P r e s s u r e \times χ_{H_{2}}$
$= 2.6 \times \frac{n_{H_{2}}}{n_{H_{2}} + n_{H e} + n_{C H_{4}}}$

$= 2.6 \times \frac{\frac{m}{2}}{\frac{m}{2} + \frac{m}{4} + \frac{m}{16}}$

$= 2.6 \times \frac{8}{13}$
$P a r t i a l P r e s s u r e_{H_{2}} = 1.6 a t m$

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