Question

The given graph represents the variation of $Z$ (compressibility factor $=\frac{P V}{n R T}$ ) versus $P$, for three real gases $A, B$ and $C .$ Identify the only incorrect statement.

• A. For the gas $A, a=0$ and its dependence on $P$ is linear at all pressures.
• B. For the gas $B, b=0$ and its dependence on $P$ is linear at all pressures.
• C. $C$ is less compressible than expected from ideal behaviour.
• D. At high pressure, the slope is positive for all real gases.

Answer 1

Answer: (C)

van der Waals equation is $\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$

When $a=0, P(V-b)=R T$ or $P V=R T+P b$

i.e., $Z=1+\frac{P b}{R T} .$ Thus, $Z>1$ and increases with increase of

pressure. Hence (a) is correct.

When $b=0,\left(P+\frac{a}{V^{2}}\right) V=R T$ or $P V+\frac{a}{V}=R T$

i.e., $Z=1-\frac{a}{R T V}$. Thus, $Z<1$ and decreases with increase of pressure. Hence, $(b)$ is correct.

Statement $(d)$ is also correct. $C$ shows negative deviation, it implies $C$ is more compressible than expected from ideal behaviour