Question

The compression factor (compressibility factor) for 1 mol of a van der Waal's gas at 0°C and 100 atmospheric pressure is found to be 0.5. Assuming that the volume of gas molecules is negligible, calculate the van der Waals constant ‘a’.

Answer 1

"Compressibility factor;

$Z\quad =\quad \frac { PV }{ nRT }$

$\Rightarrow \quad 0.5\quad =\quad \frac { 100\quad \times \quad V }{ 1\quad \times \quad 0.082\quad \times \quad 273 }$

$V\quad =\quad \frac { 0.5\quad \times \quad 0.082\quad \times \quad 273 }{ 100 }$

Or

$V\quad =\quad 0.119\quad \left( P\quad +\quad \frac {a}{{V}^{2}}\right) \left(V\quad -\quad b \right) \quad =\quad RT\quad for\quad 1\quad mol\quad$

If volume of molecule is negligible i.e., b is negligible Vander Waal's equation becomes $\left( P\quad +\quad \frac {a}{ {V}^{2}} \right) \left(V\quad -\quad 0 \right) \quad =\quad RT$

Or

$\frac {PV}{RT} \quad -\quad \frac {a\quad}{VRT} \quad =\quad 1$

Or

$a\quad =\quad \left( 1\quad -\quad \frac {PV}{RT}\right)VRT$

$a\quad =\quad (1\quad -\quad 0.5)\quad 0.1119\quad \times \quad 0.082\quad \times \quad 273$

$a\quad =\quad 1.252\quad atm{L}^{2}mol^{-2}$"

Answer 2

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HERE IS YOUR ANSWER...☺☺✌☺☺

$\huge\red{a=1.252atmL^2mol^-2}$