In van der Waals equation of state of the gas law, the constant ‘b’ is a measure of — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

# Van der Waals Equation: Understanding Constant 'b' The van der Waals equation is: $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$ **Step 1: Identify what 'b' represents physically** The term $(V - b)$ appears in the equation, where $V$ is the molar volume. This shows that 'b' is subtracted from the total volume available. **Step 2: Understand the physical meaning** In an ideal gas, molecules are treated as point particles occupying zero volume. However, real gas molecules occupy finite space. The constant 'b' accounts for the **volume occupied by gas molecules themselves** (the excluded volume). **Step 3: Relate to molecular size** Since $b$ represents the volume taken up by one mole of gas molecules: - Larger molecules → larger 'b' - Smaller molecules → smaller 'b' Therefore, **'b' is a measure of the size/volume of gas molecules** or equivalently, the **repulsive forces between molecules** (which prevent their interpenetration). **Why other options are incorrect:** - If 'b' measured attractive forces → use constant 'a' (it corrects pressure) - If 'b' measured temperature dependence → would appear differently in equation - If 'b' measured compressibility → would involve different mathematical form **Answer: C — Volume of gas molecules (or molecular size/excluded volume)**