Question

The unit of the constant ‘a’ in van der Waals equation of state of a real gas can be expressed as

• A. m\(^6\) Pa mol\(^{-2}\)
• B. m\(^3\) J mol\(^{-2}\)
• C. m\(^3\) Pa mol\(^{-2}\)
• D. m\(^3\) J mol\(^{-2}\)

Hint:

In the van der Waals equation, the constant \(a\) accounts for attractive forces between molecules and has the unit of pressure multiplied by volume squared per mole squared.

Answer 1

The Correct Option is A, D

Step 1: The van der Waals equation of state.
The van der Waals equation is given by: \[ \left( P + \frac{a}{V^2} \right) (V - b) = RT \] where \(P\) is the pressure, \(V\) is the volume, \(T\) is the temperature, \(R\) is the ideal gas constant, and \(a\) and \(b\) are constants. \(a\) accounts for intermolecular forces and has units of \(m^3 \, Pa \, mol^{-2}\) (pressure times volume squared per mole squared).
Step 2: Conclusion.
The unit of \(a\) is \(m^3 \, Pa \, mol^{-2}\), corresponding to option (C).