Question

Calculate the temperature of the gas (in kelvin) if it obeys van der Waals' equation from the following data. A flask of $2.5\text{L}$ contains $10\text{mol}$ of a gas under $50\text{atm}$. Given $(a=5.46{\text{atm L}}^2{\text{mol}}^{-2},b=0.031{\text{L mol}}^{-1})$.

Answer 1

Given:
$P=50\text{atm};V=2.5\text{L},n=10\text{mol}$; $a=5.46{\text{atm L}}^2{\text{mol}}^{-2},b=0.031{\text{L mol}}^{-1};R=0.082\text{atm L}{\text{mol}}^{-1}{\text{K}}^{-1}$
putting these values in van der Waals' equation,
$(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$
or $T=\frac{(P+\frac{a{n}^2}{V^2})(v-nb)}{nR}$
$=\frac{(50+\frac{5.46\times 100}{(2.5{)}^2})(2.5-10\times 0.031)}{10\times 0.0821}=366.4K$
on solving we get
$\therefore T=366.4K$