Question

Which of the following statements is/are correct for a gas obeying van der Waal's equation?

• A. Rise in compressibility factor with increasing pressure is due to constant 'a'.
• B. Rise in compressibility factor with increasing pressure is due to constant 'b'.
• C. Dieterici equation $[P=\frac{RT}{(V_m-b)}{e}^{-a/V_{m}RT}]$ is simply an extension of van der Waals' equations.
• D. Any equations of state, which involves only two constants in addition to R can be written in terms of reduced variables only.

Answer 1

Answer: (B), (C), (D)

The correct options are
B Rise in compressibility factor with increasing pressure is due to constant 'b'.
C Dieterici equation $[P=\frac{RT}{(V_m-b)}{e}^{-a/V_{m}RT}]$ is simply an extension of van der Waals' equations.
D Any equations of state, which involves only two constants in addition to R can be written in terms of reduced variables only.

The Dieterici equation of state is given by

$P(V-b)=RT{e}^{-a/RTV}$ and

Dieterici equation and van der Waal's equation both reduce to

$P(V-b)=RT$ at low densities.

Also, rise in compressibility factor with increasing pressure is due to constant 'b'.