Raoult's Law Calculator - Vapor Pressure of Solutions

Raoult's Law Vapor Pressure Calculator

The Raoult's law vapor pressure calculator finds the vapor pressure of a solution from two values: the mole fraction of the solvent and the vapor pressure of the pure solvent. It applies Raoult's law, a rule that describes how dissolving a non-volatile solute lowers a solvent's vapor pressure.

What is Raoult's law?

Raoult's law states that the vapor pressure of a solution equals the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent (OpenStax). A mole fraction is the share of molecules in a mixture that belong to one substance, measured as a number between 0 and 1.

The law is named after the French chemist François-Marie Raoult. It applies most simply to a non-volatile solute, a substance that does not evaporate, such as sugar. A simple picture explains the effect: solvent molecules can only evaporate from the surface, and solute particles take up part of that surface, so fewer solvent molecules escape. OpenStax notes that this picture is useful but does not explain every detail (OpenStax).

Vapor pressure lowering is one of the colligative properties, a group of solution behaviors that depend on how many solute particles are dissolved, not on what the particles are. Boiling point elevation, freezing point depression, and osmotic pressure belong to the same group (OpenStax).

Raoult's law formula

$P_{solution} = X_{solvent} \times P^{\circ}_{solvent}$

• $P_{solution}$: vapor pressure of the solution. The calculator labels pressures in kPa, but the formula works with any unit as long as both pressures use the same one.
• $X_{solvent}$: mole fraction of the solvent, a number from 0 to 1
• $P^{\circ}_{solvent}$: vapor pressure of the pure solvent at the same temperature, in the same unit as $P_{solution}$

The mole fraction of the solvent is the moles of solvent divided by the total moles in the solution:

$X_{solvent} = \frac{n_{solvent}}{n_{solvent} + n_{solute}}$

How to calculate solution vapor pressure

1. Find the mole fraction of the solvent. Divide the moles of solvent by the total moles of solvent plus solute. A solution with 80 moles of solvent and 20 moles of solute has a mole fraction of 80 / (80 + 20) = 0.8.
2. Look up the pure solvent's vapor pressure. This value depends on temperature, so it must match the temperature of the solution. Water's vapor pressure is about 3.17 kPa at 25°C but rises to about 101.3 kPa at 100°C, based on the NIST Chemistry WebBook vapor pressure equation for water.
3. Multiply the two values. The result is the solution's vapor pressure, in the same unit used for the pure solvent's vapor pressure.

Worked examples

Example 1: sugar dissolved in water

A sugar solution has a water mole fraction of 0.9 at 25°C. Pure water's vapor pressure at that temperature is 3.17 kPa.

$P_{solution} = 0.9 \times 3.17\ \text{kPa} = 2.853\ \text{kPa}$

The calculator shows 2.8530 kPa. The dissolved sugar lowers the vapor pressure from 3.17 kPa to 2.85 kPa, a drop of 10%.

Example 2: glycerin dissolved in ethanol

This example comes from OpenStax Chemistry 2e. A solution contains 92.1 g of glycerin (1.00 mol) and 184.4 g of ethanol (4.000 mol) at 40°C. Glycerin barely evaporates at this temperature. Pure ethanol's vapor pressure at 40°C is 0.178 atm.

$X_{ethanol} = \frac{4.000}{1.00 + 4.000} = 0.800$

$P_{solution} = 0.800 \times 0.178\ \text{atm} = 0.142\ \text{atm}$

To enter this in the calculator, which labels pressures in kPa, convert first: 0.178 atm × 101.325 = 18.036 kPa. With a mole fraction of 0.8, the calculator shows 14.4288 kPa, which is the same as 0.142 atm.

When Raoult's law applies

Raoult's law describes an ideal solution exactly. No real mixture is perfectly ideal, but mixtures of two very similar substances come close. Commonly quoted examples are hexane with heptane and benzene with methylbenzene (toluene) (LibreTexts).

Many real solutions deviate from the law. A positive deviation happens when the two kinds of molecules attract each other less strongly than they attract their own kind, so molecules escape into vapor more easily than predicted. Ethanol and water is the classic example. A negative deviation happens when new, stronger attractions form in the mixture, which holds molecules in the liquid and lowers vapor pressure below the prediction. A mixture of nitric acid and water is a major example (LibreTexts).

The calculator assumes only the solvent evaporates. In an ideal mixture of two volatile liquids, each component follows the law on its own, and the total vapor pressure is the sum of the partial pressures (OpenStax). For a strongly non-ideal mixture such as ethanol and water, this sum will not match measured values.

Input validation

The calculator checks both inputs before it produces a result.

• Mole fraction: must be a number from 0 to 1, inclusive. A missing or non-numeric entry, or a value outside that range, produces an error message.
• Pure solvent vapor pressure: must be a number greater than 0. Zero and negative values are rejected, since a substance's vapor pressure cannot be zero or negative.

If either input fails these checks, the calculator shows an error message and does not display a result.

Applications

Raoult's law is the starting point for designing distillation, the process of separating liquids by repeatedly evaporating and condensing a mixture. It also underlies calculations of water activity in food science, where lower vapor pressure in concentrated sugar or salt solutions helps prevent microbial growth.

For dilute solutions of a gas or trace solute, Henry's law often gives a better estimate than Raoult's law: $P_i = k_H \times X_i$, where $k_H$ is a constant specific to the solute-solvent pair. For solutions with large deviations from ideal behavior, chemists use activity coefficient models, such as the Margules, Van Laar, Wilson, NRTL, and UNIQUAC equations, which correct the formula with an added factor $\gamma_i$:

$P_i = \gamma_i \times X_i \times P^{\circ}_i$

Frequently asked questions

What is Raoult's law in simple terms? Raoult's law says that dissolving a non-volatile solute in a solvent lowers the solvent's vapor pressure in direct proportion to the solvent's mole fraction: $P_{solution} = X_{solvent} \times P^{\circ}_{solvent}$.

What values does the calculator need? It needs the solvent's mole fraction, a number between 0 and 1, and the pure solvent's vapor pressure at the working temperature, a number greater than 0.

Why does temperature matter if it is not in the formula? Temperature does not appear in the equation directly, but it strongly affects the pure solvent's vapor pressure value that goes into the equation. Using vapor pressure data from the wrong temperature gives an inaccurate result.

Why do some solutions not follow Raoult's law closely? Raoult's law assumes the solvent and solute interact with each other the same way they interact with themselves. When that is not true, actual vapor pressure rises above the prediction (positive deviation) or falls below it (negative deviation).

Can Raoult's law be used when both liquids in a mixture evaporate? Yes, for an ideal mixture. Each volatile component follows the law on its own, and the total vapor pressure is the sum of the partial pressures. The calculator handles one component at a time, so the partial pressures must be added by hand.

What happens if the mole fraction entered is 0 or 1? Both are valid. A mole fraction of 0 means no solvent is present, giving a solution vapor pressure of 0. A mole fraction of 1 means pure solvent, so the solution vapor pressure equals the pure solvent's vapor pressure.

References

1. OpenStax. Chemistry 2e, 11.4 Colligative Properties. openstax.org — statement of Raoult's law, the surface explanation, colligative properties, the sum of partial pressures, and the glycerin–ethanol example.
2. NIST. Water: Phase change data, NIST Chemistry WebBook. webbook.nist.gov — Antoine equation for the vapor pressure of water (about 3.17 kPa at 25°C and 101.3 kPa at 100°C).
3. Chemistry LibreTexts. Raoult's Law and Ideal Mixtures of Liquids. chem.libretexts.org — near-ideal pairs such as hexane–heptane and benzene–methylbenzene.
4. Chemistry LibreTexts. Non-Ideal Mixtures of Liquids. chem.libretexts.org — positive deviation (ethanol–water) and negative deviation (nitric acid–water).