Question

If the van der Waals parameters of two gases are given as:

	$a/d{m}^{6}barmo{l}^{-2}$	$b/d{m}^{3}barmo{l}^{-1}$
Gas A	6.5	0.056
Gas B	18.0	0.011

Then which of the above statements is/are correct?

• A. Critical volume of A < Critical volume of B.
• B. Critical pressure of A < Critical pressure of B.
• C. Critical temperature of A < Critical temperature of B.
• D. None of the above.

Answer 1

Answer: (B), (C)

The correct options are
B Critical pressure of A < Critical pressure of B.
C Critical temperature of A < Critical temperature of B.

as we know,
$V_c=3b,T_c=\frac{8a}{27Rb},P_c=\frac{a}{27b^2}$

For Critical Volume,
since, $b_A>b_B\Rightarrow V_{c\left(A\right)}>V_{c\left(B\right)}$
Option A is incorrect.

For Critical temperature-
Since, ${\left(\frac{a}{b}\right)}_A<{\left(\frac{a}{b}\right)}_B\Rightarrow T_{c\left(A\right)}<T_{c\left(B\right)}$
Option B is correct.

For critical pressure-
Since, ${\left(\frac{a}{b^2}\right)}_A<{\left(\frac{a}{b^2}\right)}_B\Rightarrow P_{c\left(A\right)}<P_{c\left(B\right)}$

Option C is also correct.
Hence, options B and C are correct.