What this calculator does
Raoult law says the vapour pressure of a solution is the mole fraction of the solvent multiplied by the vapour pressure of the pure solvent. One mole of solute in fifty of water drops the vapour pressure from 23.8 to 23.333 mmHg.
The solute does not need to do anything chemically. It simply occupies some of the surface, so fewer solvent molecules are positioned to escape. That is why the effect depends on how many particles are present rather than what they are, and it is the root cause of boiling point elevation and freezing point depression alike.
The formula
The solvent mole fraction is its moles divided by the total moles of everything present. Multiplying by the pure solvent vapour pressure gives the solution value, and the difference is the lowering. The law assumes an ideal solution with a non-volatile solute, so it does not apply where the solute itself evaporates.
| Term | Meaning |
|---|---|
| Raoult’s law | Vapour pressure equals solvent mole fraction times pure solvent vapour pressure. |
| Non-volatile solute | One that does not evaporate, such as salt or sugar. Required for this form of the law. |
| Vapour pressure lowering | The reduction caused by the solute, equal to the solute mole fraction times the pure value. |
| Ideal solution | One where solute-solvent interactions match solvent-solvent interactions. |
The inputs explained
| Field | What to enter |
|---|---|
| Moles of solute | Moles of solute. For a salt, count the ions it dissociates into rather than the formula units. |
| Moles of solvent | Moles of solvent. |
| Vapor pressure of pure solvent (mmHg) | Vapour pressure of the pure solvent at the temperature of interest. Water at 25 °C is 23.8 mmHg. |
When to use it
Explaining boiling point elevation
A solution with reduced vapour pressure needs a higher temperature to reach atmospheric, which is the elevation.
Determining molar mass
Measuring the vapour pressure lowering from a known mass gives the moles present and hence the molar mass.
Understanding humidity control
Saturated salt solutions hold a fixed humidity above them, which is Raoult law in practical use.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does solute lower the vapour pressure?
A range of solute amounts in the same quantity of solvent.
| Moles of solute | Vapor pressure of solution | Mole fraction of solvent | Vapor pressure lowering |
|---|---|---|---|
| 0 mol | 23.800 mmHg | 1.000 | 0.000 mmHg |
| 1 mol | 23.333 mmHg | 0.9804 | 0.467 mmHg |
| 5 mol | 21.636 mmHg | 0.9091 | 2.164 mmHg |
| 10 mol | 19.833 mmHg | 0.8333 | 3.967 mmHg |
Questions
Does Raoult’s law work for salts?
Yes, but you must count the ions rather than the formula units. Sodium chloride dissociates into two particles, so one mole of NaCl behaves as two moles of solute for this purpose. Failing to account for dissociation halves the predicted effect.
What is an ideal solution?
One where the solute and solvent interact with each other just as the solvent molecules interact among themselves. Real solutions deviate, positively when the components dislike each other and negatively when they attract, which is why the law works best for dilute solutions.
What if the solute is volatile?
Then it contributes its own vapour and the total pressure is the sum of both partial pressures, each following Raoult law separately. That is the basis of fractional distillation. This calculator assumes a non-volatile solute and does not cover that case.
How does this relate to boiling point elevation?
Directly. Boiling happens when vapour pressure reaches atmospheric pressure. Lowering the vapour pressure means a higher temperature is needed to get there, and that temperature difference is the boiling point elevation. The same lowering also explains freezing point depression.
For the resulting boiling point change, see the boiling point elevation calculator. For mole fractions, see the mole fraction calculator.