Question

Which of the following is the mathematical form of Raoult's law?

• A. \( \dfrac{P^{0}-P}{P^{0}} = \dfrac{n}{n+N} \)
• B. \( \dfrac{P^{0}-P}{P^{0}} = \dfrac{N}{n+N} \)
• C. \( \dfrac{P^{0}-P}{P} = \dfrac{n}{N+n} \)
• D. \( \dfrac{P-P^{0}}{P^{0}} = \dfrac{n}{n+N} \)

Hint:

Relative lowering of vapour pressure equals the mole fraction of the solute, \( n/(n+N) \).

Answer 1

The Correct Option is A

Step 1: Vapour pressure lowering \(\Delta P = P^{0}-P\) is caused only by the solute particles, so it must be proportional to how much of the mixture is solute.
Step 2: Dividing by the pure solvent value gives the fractional (relative) lowering \(\dfrac{P^{0}-P}{P^{0}}\).
Step 3: By Raoult's law this fraction is precisely the mole fraction of the non-volatile solute, \(x_{solute}=\dfrac{n}{n+N}\).
Step 4: Matching form, the correct expression is \(\dfrac{P^{0}-P}{P^{0}}=\dfrac{n}{n+N}\), i.e. option 1.