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 and Constant 'b' **Van der Waals equation:** $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$ **Understanding constant 'b':** The term $(V - b)$ in the equation represents the **available volume** for gas molecules to move freely. - $V$ = total volume of the container - $b$ = volume **occupied by the gas molecules themselves** **Physical meaning of 'b':** The constant $b$ accounts for the **finite size (or excluded volume) of gas molecules**. It represents the volume that is unavailable because the molecules themselves occupy space. **Why 'b' is important:** Real gas molecules are not point particles (unlike ideal gas assumptions). They have definite molecular size, so the actual free space available for molecular motion is less than the container volume. $$\text{Available volume} = V - b$$ **Conclusion:** Constant **'b' is a measure of the volume occupied by gas molecules** (or their excluded volume/molecular size). --- **Note:** Constant 'a' (in the $\frac{a}{V^2}$ term) measures **intermolecular attractive forces**, which is different from 'b'.