Question

The equation $ pv = RT $ is used for ideal gases. The right equation for real gases is van der Waals equation. What is the correct formula for the van der Waals equation? Where $\frac{a}{v^2}$ is the force of cohesion and $ b $ is the coefficient related to volume of molecules.

• A. \( \left(p + \frac{a}{v^2}\right) (v + b) = RT \)
• B. \( \left(p - \frac{a}{v^2}\right) (v - b) = RT \)
• C. \( \left(p + \frac{a}{v^2}\right) (v - b) = RT \)
• D. \( \left(p - \frac{a}{v^2}\right) (v + b) = RT \)

Hint:

The van der Waals equation corrects the ideal gas law for real gases by accounting for molecular size and intermolecular forces.

Answer 1

The Correct Option is A

Step 1: Van der Waals equation. The van der Waals equation for real gases is an adjustment to the ideal gas law.
It accounts for intermolecular forces and the finite size of molecules.
The equation is: \[ \left(p + \frac{a}{v^2}\right) (v + b) = RT \] where \( p \) is pressure, \( v \) is volume, \( T \) is temperature, \( R \) is the gas constant, \( a \) is the measure of the attraction between particles, and \( b \) is the volume occupied by the gas molecules themselves.