Question

For 1 mol of gas, the plot of pV vs. p is shown below. p is the pressure and V is the volume of the gas. What is the value of compressibility factor at point A?

• A. $1-\frac{a}{RTV}$
• B. $1+\frac{b}{V}$
• C. $1-\frac{b}{V}$
• D. $1+\frac{a}{RTV}$

Hint:

When solving compressibility factor problems: 
Start by expressing $Z = \frac{PV}{RT}$ and substitute the appropriate gas law (e.g., Van der Waals equation). 
Expand and simplify using the given conditions to isolate terms involving $V$, $a$, and $b$. 
Pay attention to the behavior of $Z$ in real gas scenarios.

Answer 1

The Correct Option is A

For 1 mole of real gas, $$PV = ZRT$$ From the graph, $PV$ for a real gas is less than $PV$ for an ideal gas at point A. Thus, $Z < 1$. The compressibility factor $Z$ is given by: $$Z = 1 - \frac{a}{V_m RT}$$ Substituting into the definition of $Z$ and simplifying: $$Z = 1 - \frac{a}{RTV}$$