A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure $P_{0}$ , volume $V_{0}$ and temperature $T_{0}$ . If the gas mixture is adiabatically compressed to a volume $V_{0} / 4$ , then the correct statement(s) is/are,
(Given $2^{1.2} = 2.3; 2^{3.2} = 9.2; R$ is gas constant)

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0.5 moles of gas A and X moles of gas B exert a pressure of 200 Pa in a container of volume 10 m3 at 1000 K. Given R is the gas constant having the units JK−1mol−1. X is :

The correct option is C 4−R2RThe total number of moles 'n' = (0.5 + X) PV = nRT n = PVRT (0.5 + X) = 200 × 101000 × R (0.5 + X) = 2R X = 2R − 12 X = 4 − R2R

$0.5$ moles of gas $A$ and $X$ moles of gas $B$ exert a pressure of $200 P a$ in a container of volume $10 m^{3}$ at $1000 K$ . Given $R$ is the gas constant having the units $J K^{-} 1 m o l^{-} 1$ . $X$ is :

The correct option is C $\frac{4 - R}{2 R}$
The total number of moles ' $n$ ' = $(0.5 + X)$

$P V = n R T$

$n = \frac{P V}{R T}$

$(0.5 + X) = \frac{200 \times 10}{1000 \times R}$

$(0.5 + X) = \frac{2}{R}$

$X = \frac{2}{R} - \frac{1}{2}$

$X = \frac{4 - R}{2 R}$