For a thermodynamically ideal solution of a non-volatile solid solute dissolved in a volatile liquid — Solutions and Colligative Properties Chemistry Question
Question
For a thermodynamically ideal solution of a non-volatile solid solute dissolved in a volatile liquid solvent, which of the following mathematical expressions correctly represent the relative lowering of vapour pressure (RLVP)? (Where $P^0$ is pure solvent VP, $P_s$ is solution VP, $n$ is moles of solute, $N$ is moles of solvent, $w, m$ are mass and molar mass of solute, $W, M$ for solvent).
💡 Solution & Explanation
Raoult's law states that RLVP equals the mole fraction of the solute: $\frac{P^0 - P_s}{P^0} = X_{solute} = \frac{n}{n+N}$ (A). Taking the reciprocal and subtracting 1 rearranges exactly to $\frac{P^0 - P_s}{P_s} = \frac{n}{N}$ (B). Expanding moles to mass/molar mass in equation (B) gives exactly $\frac{w \times M}{m \times W}$ (D). Equation (C) is a standard classical approximation strictly valid only for highly dilute solutions where $n + N \approx N$.