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. A mole fraction is the share of molecules in a mixture that belong to one substance, measured as a number between 0 and 1.

French chemist François-Marie Raoult described this relationship in 1887. He measured vapor pressure above solutions containing a non-volatile solute, a substance that does not evaporate, such as salt or sugar. He found that the vapor pressure dropped in direct proportion to how much solvent was still present. Solute particles sit at the liquid's surface and take up space, so fewer solvent molecules can escape into the air.

Raoult's law 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. Freezing point depression and osmotic pressure belong to the same group.

Raoult's law formula

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

• $P_{solution}$: vapor pressure of the solution, in any pressure unit (kPa, mmHg, atm)
• $X_{solvent}$: 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 101.3 kPa at 100°C.
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 dissolved sugar lowers the vapor pressure from 3.17 kPa to 2.85 kPa, a drop of about 10%.

Example 2: ethanol in a water mixture

A mixture has an ethanol mole fraction of 0.6 at 20°C. Pure ethanol's vapor pressure at that temperature is about 5.95 kPa.

$P_{solution} = 0.6 \times 5.95\ \text{kPa} = 3.57\ \text{kPa}$

This gives ethanol's own contribution to the total vapor pressure. Because water also evaporates, its partial pressure must be calculated separately, using water's mole fraction (0.4) and its own pure vapor pressure, then added to get the total pressure above the mixture.

When Raoult's law applies

Raoult's law describes an ideal solution exactly. Real solutions match it closely when the solvent and solute have similar molecular structure and similar intermolecular forces, such as benzene mixed with toluene.

Many real solutions deviate from the law. A positive deviation happens when solvent and solute molecules attract each other less strongly than they attract their own kind; molecules escape into vapor more easily than predicted. A negative deviation happens when the two substances attract each other strongly, for example through hydrogen bonding, as in a chloroform-acetone mixture; this holds molecules in the liquid and lowers vapor pressure below the prediction.

Raoult's law also assumes only one component evaporates. For a mixture of two volatile liquids, such as ethanol and water, each component follows the law separately, and the total pressure is the sum of both partial pressures.

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. In pharmaceutical manufacturing, it helps predict how fast solvents evaporate during drying steps such as freeze-drying.

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. Each volatile component follows the law on its own. The mixture's total vapor pressure is the sum of the partial pressures of each component.

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. Atkins, P. W., & de Paula, J. (2014). Atkins' Physical Chemistry (10th ed.). Oxford University Press.
2. Smith, J. M., Van Ness, H. C., & Abbott, M. M. (2017). Introduction to Chemical Engineering Thermodynamics (8th ed.). McGraw-Hill Education.
3. Raoult, F. M. (1887). "Loi générale des tensions de vapeur des dissolvants." Comptes Rendus de l'Académie des Sciences, 104, 1430–1433.
4. NIST Chemistry WebBook — vapor pressure data for common solvents.
5. IUPAC Gold Book — definitions for Raoult's law and related terms.