Question

$T_c$ and $P_c$ of a gas are $400\text{K}$ and $41$ atm respectively, $V_c$ is:

• A. $\frac{400R}{41}$
• B. $\frac{150R}{41}$
• C. $\frac{41R}{400}$
• D. $\frac{300R}{41}$

Answer 1

The correct option is B $\frac{150R}{41}$

According to van der Waals' equation,
constants 'a' and 'b' in terms of pressure, molar volume and temperature at critical point are related as
$b=\frac{R{T}_c}{8P_c}$....(1)
and molar volume $V_c=3b$....(2)
put up the values of $T_{c}and{P}_c$ in eq (1) from where we get
$b=\frac{R\times 400}{8\times 41}=\frac{50R}{41}$
put up in eq(2) we get
$V_c=3\times \frac{50R}{41}=\frac{150R}{41}$
Hence option is option (b).