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Real Gases

SO2 and NH3...

Question

$S O_{2}$ and $N H_{3}$ have critical temperatures of $430.7 K$ and $405.6 K$ , respectively. $P_{C}$ for $S O_{2} = 77.76$ atm and $P_{C}$ for $N H_{3} = 111.5$ atm. The ratio $b_{S O_{2}} : b_{N H_{3}}$ is:

A

2 : 3

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B

1 : 1

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C

2 : 1

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D

3 : 2

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Solution

The correct option is D $3 : 2$
$T_{C} = \frac{8 a}{27 b R}$ ; $P_{C} = \frac{a}{27 b^{2}}$
$∴ \frac{T_{C}}{P_{C}} = \frac{8 b}{R}$
$\Rightarrow b = \frac{R T_{C}}{8 P_{C}}$
$∴ \frac{b_{S O_{2}}}{b_{N H_{3}}} = \frac{430.7 \times 111.5}{77.76 \times 405.6} = \frac{3}{2}$
$3 : 2$ .

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