# Raoult's law

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Established by François-Marie Raoult in 1882[1], Raoult's law states:

Once the components in the solution have reached equilibrium, the total vapor pressure p of the solution is:

and the individual vapor pressure for each component is

where

Consequently, as the number of components in a solution increases, the individual vapor pressures decrease, since the mole fraction of each component decreases with each additional component. If a pure solute which has zero vapor pressure (it will not evaporate) is dissolved in a solvent, the vapor pressure of the final solution will be lower than that of the pure solvent.

This law is strictly valid only under the assumption that the chemical interactions between the two liquids is equal to the bonding within the liquids: the conditions of an ideal solution. Therefore, comparing actual measured vapor pressures to predicted values from Raoult's law allows information about the relative strength of bonding between liquids to be obtained. If the measured value of vapor pressure is less than the predicted value, fewer molecules have left the solution than expected. This is put down to the strength of bonding between the liquids being greater than the bonding within the individual liquids, so fewer molecules have enough energy to leave the solution. Conversely, if the vapor pressure is greater than the predicted value more molecules have left the solution than expected, due to the bonding between the liquids being less strong than the bonding within each.

The vapor pressure and composition in equilibrium with a solution can yield valuable information regarding the thermodynamic properties of the liquids involved. Raoult’s law relates the vapor pressure of components to the composition of the solution. The law assumes ideal behavior. It gives a simple picture of the situation just as the ideal gas law does. The ideal gas law is very useful as a limiting law. As the interactive forces between molecules and the volume of the molecules approaches zero, so the behavior of gases approach the behavior of the ideal gas.

Raoult’s law is similar in that it assumes that the physical properties of the components are identical. The more similar the components are, the more their behavior approaches that described by Raoult’s law. For example, if the two components differ only in isotopic content, then the vapor pressure of each component will be equal to the vapor pressure of the pure substance P0 times the mole fraction in the solution. This is Raoult’s law.

Using the example of a solution of two liquids, A and B, if no other gases are present, then the total vapor pressure p above the solution is equal to the weighted sum of the "pure" vapor pressures of the two components, pA and pB. Thus the total pressure above solution of A and B would be

## Contents

### Derivation

We define an ideal solution as a solution for which the chemical potential of component i is:

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