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 Analysis **Step 1: Identify the van der Waals equation** $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$ The constant $b$ represents the volume occupied by one mole of gas molecules themselves (excluded volume). **Step 2: Determine dimensional consistency** Since $b$ is subtracted from $V$ (molar volume): $$V - b$$ Both terms must have the same dimensions. Therefore, $b$ has **dimensions of volume**. **Step 3: Express in standard units** For one mole of gas: - $V$ is in $\text{L/mol}$ or $\text{cm}^3\text{/mol}$ - Therefore, $b$ is in $\text{L/mol}$ or $\text{cm}^3\text{/mol}$ In SI units: $b$ is in $\text{m}^3\text{/mol}$ **Answer: C** corresponds to **$\text{L/mol}$** or **$\text{cm}^3\text{/mol}$** (volume per mole) This makes physical sense: $b$ quantifies the volume unavailable for gas molecules due to their own molecular volume, expressed per mole of substance.