The units of the van der Waal’s constant ‘a’ are — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

# Van der Waals Constant 'a' Units **Step 1: Identify the van der Waals equation** The van der Waals equation is: $$\left(P + \frac{a}{V_m^2}\right)(V_m - b) = RT$$ where $V_m$ is molar volume. **Step 2: Analyze dimensional consistency** For the equation to be dimensionally valid, the term $\frac{a}{V_m^2}$ must have units of **pressure**. $$\frac{[a]}{[V_m]^2} = [P]$$ **Step 3: Solve for units of 'a'** $$[a] = [P] \times [V_m]^2$$ Substituting SI units: - $[P]$ = Pa (or $\text{N/m}^2$) - $[V_m]$ = $\text{m}^3/\text{mol}$ $$[a] = \text{Pa} \times (\text{m}^3/\text{mol})^2 = \text{Pa·m}^6/\text{mol}^2$$ **Step 4: Convert to common units** In SI base units: $$[a] = \frac{\text{N}}{\text{m}^2} \times \frac{\text{m}^6}{\text{mol}^2} = \boxed{\text{N·m}^4/\text{mol}^2 \text{ or Pa·m}^6/\text{mol}^2}$$ **Answer A** correctly identifies these units. The constant 'a' accounts for intermolecular attractive forces and has dimensions of pressure × (volume)².