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: \[ Z = 1 - \frac{a}{RTV} \]