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Limitation of Dimensional Analysis

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Question

calculate from the Van der Waal's equation,the temperature at which 128 gm of $S O_{2}$ would occupy a vol. of $10 d m^{3}$ at 15 atm pressure:[a=25atm $l i t^{2} m o l^{2}, b = 0.05 l i t m o l^{- 1}]$

A

700^{\circ} C

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B

717^{\circ} C

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C

930^{\circ} C

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D

692^{\circ} C

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Solution

The correct option is A $692^{\circ} C$
The number of moles of $S O_{2} = \frac{128}{64} = 2$
The van der waals equation for real gases is
$(P + \frac{a n^{2}}{V^{2}}) (V - n b) = R T$
Substitute values in the above equation.
$(15 + \frac{25 \times 2^{2}}{(10)^{2}}) (10 - 2 \times 0.05) = 0.082 \times T$
$T = 965 K = 965 - 273 = 692^{o} C$

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