Question

Arrange the following gases in increasing order of their critical temperatures: A. $W (a=4.0, b=0.027)$, B. $X (a=8.0, b=0.030)$, C. $Y (a=6.0, b=0.032)$, D. $Z (a=12, b=0.027)$.

• A. D, B, C, A
• B. A, C, B, D
• C. D, B, A, C
• D. B, C, D, A

Hint:

High 'a' (attraction) and low 'b' (size) make a gas much easier to liquefy (Higher $T_{c}$).

Answer 1

The Correct Option is B

Step 1: Concept Critical Temperature ($T_{c}$) is calculated using the formula $T_{c} = \frac{8a}{27Rb}$.

Step 2: Meaning Since $8$ and $27R$ are constants, $T_{c} \propto \frac{a}{b}$.

Step 3: Analysis Calculate $a/b$ ratios: W: $4/0.027 \approx 148.1$. X: $8/0.030 \approx 266.7$. Y: $6/0.032 \approx 187.5$. Z: $12/0.027 \approx 444.4$.

Step 4: Conclusion Sorting ratios in increasing order: $148.1 (W) < 187.5 (Y) < 266.7 (X) < 444.4 (Z)$. This matches the order A $<$ C $<$ B $<$ D. Final Answer: (B)