Question

The Van der Waals constants for gases A, B and C are as follows

Gas	a[/atm L² mol⁻²]	b[/L mol⁻¹]
A	8.21	0.050
B	4.105	0.030
C	1.682	0.040

Which gas has (i) the highest critical temperature, (ii) the largest molecular volume, and (iii) most ideal behaviour around 500 K?

• A. (i) A, (ii) A, (iii) C
• B. (i) B, (ii) A, (iii) A
• C. (i) C, (ii) B, (iii) B
• D. (i) A, (ii) C, (iii) B

Answer 1

Answer: (A)

(i) A, (ii) A, (iii) C

Answer 2

1. Highest Critical Temperature ($T_c$): $T_c \propto \frac{a}{b}$.

   • Gas A: $\frac{8.21}{0.050} = 164.2$
   • Gas B: $\frac{4.105}{0.030} \approx 136.83$
   • Gas C: $\frac{1.682}{0.040} = 42.05$ Gas A has the highest $\frac{a}{b}$ ratio, hence the highest $T_c$.

2. Largest Molecular Volume: This is directly proportional to the Van der Waals constant 'b'.

   • Gas A: $b = 0.050$ L mol⁻¹
   • Gas B: $b = 0.030$ L mol⁻¹
   • Gas C: $b = 0.040$ L mol⁻¹ Gas A has the largest 'b' value, hence the largest molecular volume.

3. Most Ideal Behaviour around 500 K: Ideal behaviour is observed near the Boyle temperature ($T_B = \frac{a}{Rb}$).

   • Gas A: $T_B = \frac{8.21}{0.0821 \times 0.050} = 2000$ K
   • Gas B: $T_B = \frac{4.105}{0.0821 \times 0.030} \approx 1667$ K
   • Gas C: $T_B = \frac{1.682}{0.0821 \times 0.040} \approx 512$ K Gas C's Boyle temperature (512 K) is closest to 500 K, indicating it will behave most ideally at this temperature.