Outline
In a mixed solution of two or more components, the law that the partial pressure is proportional to the product of the vapor pressure of the pure substance and the concentration of that substance is called Raoult's law, and such a solution is called an ideal solution.
It is easier and more comprehensible with formulas than with text.
For example, the partial pressures p1 and p2 of the first and second components are expressed by the following equations.
$$p_{1}=P_{1}x_{1}$$
$$p_{2}=P_{2}x_{2}$$
where p1 is the partial pressure of the first component, p2 is the partial pressure of the second component, P1 is the vapor pressure of the pure substance of the first component, P2 is the vapor pressure of the pure substance of the second component, x1 is the molar liquid fraction of the first component, x2 is the molar liquid fraction of the first component.
Although a two-component system is given as an example, the same can be applied to systems with three or more components.
$$p_{i}=P_{i}x_{i}$$
where pi is the partial pressure of the i component, Pi is the vapor pressure of the pure substance of the i component, xi is the molar liquid fraction of the i component.
Extension to non-ideal solutions
Raoult's law only holds for systems in which there is no interaction between the components.
Only some combinations, such as hydrocarbon compounds under low pressure conditions, exhibit behavior similar to ideal solutions.
On the other hand, compounds with polar molecules such as water and alcohols exhibit non-ideal behavior, so Raoult's law does not hold. However, Raoult's law is very important even for such non-ideal solutions.
This is because the partial pressure of a non-ideal solution is generally expressed by multiplying Raoult's law by a correction factor, so the form of the base equation is the same as Raoult's law.
$$p_{i}=P_{i}x_{i}γ_{i}$$
where γi is the Activity coefficient of i component.
γi is the correction factor, specially called the activity coefficient.
This activity coefficient corrects the partial pressure calculated from the ideal solution to the actual partial pressure.
Therefore, if you want to calculate the partial pressure of a non-ideal solution, you need to calculate the activity coefficient γ separately.
How to accurately determine the activity coefficient γ is where chemical engineers show their skills, and is one of the most difficult issues in the field of physical property estimation as a whole.
Research is still ongoing in the academic field, and new models for estimating activity coefficients have been published in recent years.