Question

Two gases have same value of ‘a’ but different value of ‘b’ therefore which of the following is/are correct ?

• A. Both the gases have equally compressible
• B. Both the gases are incompressible
• C. Gas having greater value of ‘b’ is more compressible
• D. Gas having lesser value of b is more compressible

Answer 1

Answer: (D)

Gas having lesser value of b is more compressible

Answer 2

As per vanderwaals equation ,

$\left( P + \frac{a}{V_{m}^{2}} \right)$ $\left( V_{m} - b \right)$ = RT

or P = $\frac{RT}{(V_{m} - b)}$ – $\frac{a}{V_{m}^{2}}$

or $\frac{PV_{m}}{RT}$ = Z = $\frac{V_{m}}{(V_{m} - b)}$– $\frac{a}{RTV_{m}}$

or Z = $\left( 1 - \frac{b}{V_{m}} \right)^{- 1}$ – $\frac{a}{RTV_{m}}$ ~ 1 + $\left( b - \frac{a}{RT} \right)$

$\frac{1}{V_{m}}$ +……

Neglecting the higher terms

Z ~ 1 + $\left( b - \frac{a}{RT} \right)$ $\frac{1}{V_{m}}$

For more compressible gas Z is lesser , hence the value of b should be lesser