Question

The Vander Waals equation of state is given by:

• A. \( P = \frac{RT}{(v - b)} - \frac{a}{T^{0.5} v (v + b)} \)
• B. \( P = \frac{RT}{(v - b)} - \frac{a}{v^2} \)
• C. \( P = \frac{RT}{(v - b)} - \frac{{a'}{T}}{v(v + b)} \)
• D. \( P = \frac{RT}{(v - b)} - \frac{a \alpha}{v(v + b) + b(v - b)} \)

Hint:

The Vander Waals equation corrects for ideal gas behavior by accounting for the volume occupied by molecules and intermolecular forces. The equation is crucial for describing real gases.

Answer 1

The Correct Option is B

Step 1: Vander Waals Equation of State.
The Vander Waals equation of state is an equation of state for real gases that accounts for the finite size of molecules and intermolecular attractions. The equation is given by: \[ P = \frac{RT}{v - b} - \frac{a}{v^2} \] where:
\( P \) is the pressure,
\( R \) is the ideal gas constant,
\( T \) is the temperature,
\( v \) is the molar volume of the gas,
\( a \) is the measure of the attraction between particles,
\( b \) is the volume occupied by the gas molecules.
Step 2: Understand the terms.
The first term \(\frac{RT}{v - b}\) accounts for the ideal gas behavior, correcting for the finite size of molecules by subtracting \( b \) from the molar volume.
The second term \(\frac{a}{v^2}\) corrects for intermolecular attractions between gas molecules.
Step 3: Identify the correct option.
From the options provided, the correct form of the Vander Waals equation is: \[ P = \frac{RT}{(v - b)} - \frac{a}{v^2}. \] Final Answer: The correct form of the Vander Waals equation is \( P = \frac{RT}{(v - b)} - \frac{a}{v^2} \).