Question

Figure displays the plot of the compression factor $Z$ verses $P$ for a few gases.
Which of the following statements is/are correct for a vander walls gas:

• A. The plot $I$ is applicable provided the vander waals constant $a$ is negligible.
• B. The plot $II$ is applicable provided the vander waals constant $b$ is negligible.
• C. The plot $III$ is applicable provided the vander waals constant $a$ and $b$ are negligible.
• D. The plot $IV$ is applicable provided the temperature for the gas is much higher than its critical temperature.

Answer 1

Answer: (A), (B), (C)

The correct options are
A The plot $I$ is applicable provided the vander waals constant $a$ is negligible.
B The plot $II$ is applicable provided the vander waals constant $b$ is negligible.
C The plot $III$ is applicable provided the vander waals constant $a$ and $b$ are negligible.

The vander waals equation of state is: {for 1 mole of gas} $\left(P+a/V_m^2\right)\left(V_m-b\right)=RT$ When a is negligible, then $Z=p{V}_m/RT=1+b/(RTP)$ that is $Z$ increases with increase in $p$. when $b$ is negligible, then $Z=p{V}_m/RT=1-a/\left(VRT\right)$ increasing $p$ implies decreases in $V$, which is turn, implies increase in the value of $a/VRT$ and hence decrease in the value of $Z$. The curve IV is applicable provided temperature of the gas is near bit larger than it's critical temperature Hence, three choice A,B,C are correct.