If z is the compressibility factor, then for Van der Walls equation ans. z = 1 - RT/Pb z = 1 –Pb/RT z = 1 + RT/Pb z = 1 – a/VRT

The question asks for the correct expression for the compressibility factor $z$ in relation to the Van der Waals equation.

Based on the context of the question, here's the analysis:

Understanding the Van der Waals Equation

The Van der Waals equation is given by:

$(P + a \frac{n^2}{V^2})(V - nb) = nRT$

Where:

• $P$ = pressure
• $V$ = volume
• $n$ = number of moles
• $R$ = universal gas constant
• $T$ = temperature
• $a$ = measure of the attractive forces between molecules
• $b$ = volume occupied by one mole of particles

Analysis of Compressibility Factor

The compressibility factor $z$ is defined as:

$z = \frac{PV}{nRT}$

Examining the Options

To evaluate each provided expression:

1. Option 1: $z = 1 - \frac{RT}{Pb}$
2. Option 2: $z = 1 - \frac{Pb}{RT}$
3. Option 3: $z = 1 + \frac{RT}{Pb}$
4. Option 4: $z = 1 - \frac{a}{VRT}$

Verification of Each Expression

• The correct form of the compressibility factor often derived from the Van der Waals equation upon rearranging terms may lean towards expressions that have similar forms to $z = 1 - \frac{a}{VRT}$ relating to the non-ideality of gases.

Final Answer

Out of the given options regarding the compressibility factor $z$ in relation to the Van der Waals equation, the most appropriate choice is:

$z = 1 - \frac{a}{VRT}$ Thus, the correct answer is the fourth option:

Final Answer: $z = 1 - \frac{a}{VRT}$