Grade 12 Chemistry · Vapour pressure stories
Three straight lines and one curve
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Three straight lines and one curve

Above every liquid sits a vapour, and three laws tell you how much.

Raoult's law, P=xP0P = x\,P^{0}P equals x P-nought. PP is the vapour pressure of the solvent above the solution, P0P^{0} (say “P-nought”) is the vapour pressure of the pure solvent at that temperature, and xx is the mole fraction of the SOLVENT — not the solute. That is the structural trap of this lesson, and it is worth saying twice: Raoult reads the solvent's fraction, because the solvent is what evaporates. Dissolve something non-volatile and x<1x < 1, so PP always falls below P0P^{0}. That drop is why the boiling point had to climb in the last lesson.

Henry's law, C=HPC = HP, runs the other direction: a gas dissolving INTO a liquid. CC is the dissolved concentration in mol/m³, PP is that gas's partial pressure above the liquid in pascals, and HH is the Henry solubility constant in mol/(m³·Pa) — 1.3 × 10⁻⁵ for oxygen in water at 25 °C, 3.3 × 10⁻⁴ for carbon dioxide, which is precisely why a bottle fizzes when you release the pressure above it. Note the pascals: HH is quoted per Pa, so kilopascals must be converted before they go in.

The curve is Clausius–Clapeyron, two-point form: ln ⁣(P2P1)=ΔHvapR(1T21T1)\ln\!\left(\dfrac{P_2}{P_1}\right) = -\dfrac{\Delta H_{vap}}{R}\left(\dfrac{1}{T_2} - \dfrac{1}{T_1}\right). P1P_1 and P2P_2 are the pure liquid's vapour pressures at absolute temperatures T1T_1 and T2T_2 — subscripts back to naming two STATES of one liquid — and ΔHvap\Delta H_{vap} is its molar enthalpy of vaporisation in J/mol, with R=8.314 J/(molK)R = 8.314\ \mathrm{J/(mol \cdot K)}. Vapour pressure climbs exponentially with temperature, which is why the plot that straightens it is lnP\ln P against 1/T1/T, and why water boils at 71 °C on top of Everest. Two units to guard: ΔH\Delta H in joules to match R, and every T in kelvin, because a reciprocal temperature is meaningless from any other zero.