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The van der Waals' equation for $0.5 \mathrm{~mol}$ of a gas is
Options:
Solution:
2780 Upvotes
Verified Answer
The correct answer is:
$\left(p+\frac{a}{4 V^2}\right)(2 V-b)=R T$
van der Waals' equation is
$$
\left(p+\frac{a n^2}{V^2}\right)(V-n b)=n R T
$$
where, $\quad a=$ correction in pressure
$b=$ correction in volume
$n=$ number of moles
Given, $\quad n=0.5 \mathrm{~mol}$
$$
\left(p+\frac{a(0.5)^2}{V^2}\right)(V-0.5 b)=0.5 R T
$$
or $\quad\left(p+\frac{a}{4 V^2}\right)(2 V-b)=R T$
Thus, option (2) is correct.
$$
\left(p+\frac{a n^2}{V^2}\right)(V-n b)=n R T
$$
where, $\quad a=$ correction in pressure
$b=$ correction in volume
$n=$ number of moles
Given, $\quad n=0.5 \mathrm{~mol}$
$$
\left(p+\frac{a(0.5)^2}{V^2}\right)(V-0.5 b)=0.5 R T
$$
or $\quad\left(p+\frac{a}{4 V^2}\right)(2 V-b)=R T$
Thus, option (2) is correct.
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