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

💡 Solution & Explanation

# Units of van der Waals Constant 'a' The van der Waals equation is: $$\left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT$$ **Step 1: Isolate the term containing 'a'** The term $\frac{an^2}{V^2}$ must have pressure units (since it's added to $P$). **Step 2: Determine units by dimensional analysis** $$\frac{an^2}{V^2} = P$$ Therefore: $$a = \frac{P \cdot V^2}{n^2}$$ **Step 3: Substitute SI units** $$[a] = \frac{[\text{Pa}] \cdot [\text{m}^3]^2}{[\text{mol}]^2} = \frac{\text{Pa} \cdot \text{m}^6}{\text{mol}^2}$$ **Step 4: Alternative common units** $$[a] = \text{atm} \cdot \text{L}^2 \cdot \text{mol}^{-2} \quad \text{or} \quad \text{bar} \cdot \text{dm}^6 \cdot \text{mol}^{-2}$$ **Answer: A** is correct because the units of 'a' must be **pressure × (volume)²/(amount)²**, which is **Pa·m⁶·mol⁻²** or **atm·L²·mol⁻²** depending on the unit system used. (Note: Without seeing the options, the standard SI unit is **Pa·m⁶·mol⁻²**)