Consider the composite system, which is held at $300$ K, shown in the following figure. Assuming ideal gas behaviour, calculate the total pressure if the barriers separating the compartments are removed. Assume that the volume of the barriers is negligible.(Given $r = 0.082$ atm L/mol.K).

1

atm

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2

atm

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2.3

atm

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3.2

atm

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Solution

The correct option is B $2$ atm
The number of moles of $H e, N e$ and $X e$ is given by
$n_{H e} = \frac{P V}{R T} = \frac{3}{R T},$ $n_{N e} = \frac{P V}{R T} = \frac{10}{R T},$

$n_{X e} = \frac{P V}{R T} = \frac{1}{R T},$
$n = n_{H e} + n_{N e} + n_{X e} = \frac{(3 + 10 + 1)}{R T}$

The total pressure is given by
$P = \frac{(n_{H e} + n_{N e} + n_{X e})}{R} T V$
$P_{total} = \frac{(3 + 10 + 1)}{R T} \times \frac{R T}{7} = 2 a t m$

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