How this instrument works
Raoult's law states that the vapor pressure of a solution, P_solution, equals the vapor pressure of the pure solvent, P_pure_solvent, multiplied by the solvent's mole fraction in the solution, x_solvent. Dissolving a non-volatile solute — one that doesn't itself evaporate, like sugar or salt in water — dilutes the solvent molecules at the liquid's surface, so fewer of them escape into vapor per unit time than would from the pure solvent alone, and vapor pressure falls in direct proportion to how much of the solution, by mole fraction, is still solvent.
The mechanism is a straightforward crowding effect at the liquid surface. In pure solvent, every molecule at the surface is a solvent molecule capable of evaporating; add solute, and some of the surface positions are now occupied by solute particles instead, which (for a non-volatile solute) don't contribute to the vapor above the liquid. If the solvent makes up 90% of the solution by mole fraction, only about 90% as many solvent molecules escape per unit time compared to pure solvent, and vapor pressure falls to about 90% of its pure-solvent value — exactly what x_solvent x P_pure_solvent captures.
François-Marie Raoult proposed the law in 1887 from careful vapor-pressure measurements, and it holds most closely for ideal solutions — mixtures where solute and solvent molecules interact with each other about as strongly as they interact with their own kind. Real solutions deviate: if solute-solvent attraction is unusually strong, vapor pressure falls below Raoult's-law prediction (a negative deviation); if solute and solvent molecules would rather associate with their own kind, vapor pressure runs higher than predicted (a positive deviation). Raoult's law is also the foundation behind boiling-point elevation and freezing-point depression, since both those colligative properties trace back to this same vapor-pressure suppression.
- Enter the solvent's share of the solution into Mole fraction of solvent — a number between 0 and 1, closer to 1 for a dilute solution.
- Enter the pure solvent's vapor pressure at your working temperature into Vapor pressure of pure solvent (mmHg) — a tabulated value, such as water's roughly 23.8 mmHg at 25 degrees C.
- Read Vapor pressure of the solution (mmHg) — the lowered vapor pressure the actual solution exhibits.
- To see how additional solute changes vapor pressure, lower Mole fraction of solvent (adding more solute reduces the solvent's own share) and watch the result fall.
- This calculation assumes the solute itself is non-volatile; a volatile solute would also contribute its own vapor pressure, which this instrument doesn't account for.
Worked example — 10% solute by mole fraction in water at 25°C
Enter 0.9 into Mole fraction of solvent and 23.8 into Vapor pressure of pure solvent (mmHg) — water's approximate vapor pressure at 25 degrees C, with a non-volatile solute making up the remaining 10% of the solution by mole fraction. Vapor pressure of the solution (mmHg) reads 21.4200: the instrument multiplies 0.9 x 23.8 = 21.42.
The solution's vapor pressure has dropped by 2.38 mmHg from pure water's 23.8 mmHg — exactly 10% lower, matching the 10% of the solvent's mole fraction that solute now occupies. Set Mole fraction of solvent to 1 (no solute at all) and Vapor pressure of the solution (mmHg) returns to 23.8000, the pure solvent's own vapor pressure, as it must.
Questions
Why does adding solute lower the vapor pressure instead of raising it?
Because a non-volatile solute takes up some of the space at the liquid's surface without itself evaporating. In pure solvent, every surface molecule is a potential contributor to the vapor; once solute particles occupy part of that surface, fewer solvent molecules are available to escape per unit time, so the equilibrium vapor pressure — a balance between evaporation and condensation — settles at a lower value than the pure solvent's.
How is this related to boiling-point elevation and freezing-point depression?
Both trace back to this same vapor-pressure suppression. A liquid boils when its vapor pressure reaches atmospheric pressure, so a solution with lowered vapor pressure needs a higher temperature to reach that same point, producing boiling-point elevation. Freezing-point depression follows a related argument involving the solid-liquid equilibrium. Both are colligative properties, meaning they depend on how much solute is dissolved (its mole fraction), not on what the solute chemically is.
Does Raoult's law apply if the solute is volatile too?
The law extends to that case, but this calculator's simple x_solvent x P_pure_solvent form assumes a non-volatile solute contributing nothing to the vapor. For a mixture of two volatile liquids, both components follow Raoult's law simultaneously — each contributes its own partial vapor pressure (its mole fraction times its own pure vapor pressure) — and the solution's total vapor pressure is the sum of both contributions, similar in spirit to Dalton's law for gas mixtures.
Is this the same formula as Dalton's law of partial pressures?
The arithmetic looks identical — a mole fraction times a pressure — but the two describe different physical situations. Dalton's law finds a gas's contribution to a mixture's total pressure from its mole fraction within that gas mixture. Raoult's law finds a liquid solution's vapor pressure from the solvent's mole fraction within the liquid phase, referenced against the pure solvent's own vapor pressure rather than a total. They share a formula shape because both describe a component's fractional share of some whole, but the 'whole' being divided is a different physical quantity in each case.
Why do real solutions sometimes deviate from Raoult's law?
Raoult's law assumes an ideal solution, where solute-solvent interactions are about as strong as solvent-solvent interactions. When a solute interacts with the solvent more strongly than expected (hydrogen bonding, for instance), it holds solvent molecules at the surface more tightly than pure solvent would, and measured vapor pressure comes in below the law's prediction — a negative deviation. When solute and solvent would rather avoid each other, vapor pressure runs above the prediction instead, a positive deviation.
What vapor pressure should I use for the pure solvent?
The pure solvent's vapor pressure at the same temperature the solution is being evaluated at — vapor pressure is strongly temperature-dependent, so a value measured or tabulated at a different temperature will give a misleading result. Chemistry reference tables list vapor pressure of water and other common solvents across a range of temperatures for exactly this reason.