Hong Life CalculatorsUnderstanding the Raoult's law calculator — concept and principle
This calculator applies Raoult's law to find the vapour pressure of a solution containing a nonvolatile solute, the vapour-pressure lowering and the mole fractions. It accounts for electrolytes through the van 't Hoff factor. It is used in general and physical chemistry for colligative properties.
How it is calculated
n_solvent = solvent mass ÷ molar mass; n_particles = (solute mass ÷ molar mass) × i
X_solvent = n_solvent ÷ (n_solvent + n_particles)
P_solution = X_solvent × P*; ΔP = P* − P_solution = X_solute × P*
- The result is in whatever unit you enter for P*.
The principle
Molecules escape from a liquid's surface into the vapour. Dissolving a nonvolatile solute means some of the surface is occupied by solute particles that do not evaporate, so fewer solvent molecules escape per second. In an ideal solution the vapour pressure falls in direct proportion to the solvent's mole fraction. The lowering depends only on how many particles are dissolved, not what they are, which makes it a colligative property like boiling-point elevation.
Worked example
Default inputs: 100 g glucose (180.16 g/mol), i = 1, 500 g water (18.015 g/mol), P* = 23.76 (mmHg, water at 25 °C).
- Solute particles = 100 ÷ 180.16 = 0.5551 mol; solvent = 500 ÷ 18.015 = 27.75 mol.
- X_solvent = 27.75 ÷ 28.31 = 0.9804; X_solute = 0.0196.
- P = 0.9804 × 23.76 = 23.29.
- Lowering ΔP = 0.4659, a relative lowering of 1.96%.
| Vapor pressure of the pure solvent P* (any unit) | Vapor pressure of the solution (unit of P*) |
|---|---|
| 5.94 | 5.824 |
| 11.9 | 11.65 |
| 17.8 | 17.47 |
| 23.8 | 23.29 |
| 29.7 | 29.12 |
| 35.6 | 34.94 |
| 47.5 | 46.59 |
How to read the result
The relative lowering equals the solute particle mole fraction. Doubling the solute roughly doubles the lowering in dilute solutions. Salts split into ions, so the same moles of NaCl lower the vapour pressure about twice as much as glucose.
Common mistakes
- Forgetting the van 't Hoff factor for salts.
- Using mass fraction instead of mole fraction.
- Applying the formula to volatile solutes, which add their own vapour.
Frequently asked questions
Why does a solute lower vapour pressure?
Fewer solvent molecules are at the surface to escape.
Is the lowering the same for all solutes?
For ideal dilute solutions it depends only on the number of dissolved particles.
What unit is the result in?
The same unit you entered for P*.
How is this related to boiling-point elevation?
Lower vapour pressure means the solution must be heated more to reach atmospheric pressure.
Sources: OpenStax, Chemistry: Atoms First 2e, section 11.4 "Colligative Properties"