States of Matter 1 Question 71
71. Calculate the pressure exerted by one mole of $\mathrm{CO}{2}$ gas at $273 \mathrm{~K}$ if the van der Waals’ constant $a=3.592 \mathrm{dm}^{6} \mathrm{~atm}$ $\mathrm{mol}^{-2}$. Assume that the volume occupied by $\mathrm{CO}{2}$ molecules is negligible.
(2000)
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Answer:
Correct Answer: 71. $(6.46)$
Solution:
- In case of negligible molecular volume, $b=0$ and van der Waals’ equation reduces to
$$ \begin{aligned} \left(p+\frac{n^{2} a}{V^{2}}\right) V & =n R T \ \Rightarrow \quad p & =\frac{R T}{V}-\frac{a}{V^{2}} \quad(n=1 \text { mole }) \ & =\frac{0.082 \times 273}{22.4}-\frac{3.592}{(22.4)^{2}}=0.99 \mathrm{~atm} \end{aligned} $$
