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

💡 Solution & Explanation

# Van der Waals Constant 'b' Units **Step 1: Recall the van der Waals equation** $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$ where $V$ is molar volume. **Step 2: Analyze dimensional consistency** Since $(V - b)$ is a subtraction, both $V$ and $b$ must have **identical dimensions**. Molar volume $V$ has units of **volume per mole**: $\text{L·mol}^{-1}$ or $\text{m}^3\text{·mol}^{-1}$ **Step 3: Determine units of b** Therefore, $b$ must also have units of **volume per mole**: $$\boxed{b \text{ has units of } \text{L·mol}^{-1} \text{ or } \text{cm}^3\text{·mol}^{-1}}$$ **Physical meaning:** The constant $b$ represents the excluded volume per mole of gas molecules due to their finite size. It accounts for the volume occupied by gas particles themselves. --- *Note: Without seeing the options, the correct answer should be whichever option represents volume per mole (likely expressed as L/mol, cm³/mol, or dm³/mol).*