User:R0ck$/Relative lowering of vapor pressure

Relative lowering of vapor pressure is a drop in the vapor pressure of a substance, caused when a smaller amount of another, non-volatile substance is added. .

In all cases, the substance added/present in smaller amounts is considered the solute, while the original substance present in larger quantity is thought of as the solvent. The partial pressure of the solvent decreases due to a decrease in the amount of solvent particles present near the surface of the mixture, caused by a decrease in solvent concentration.

Using vapor pressure
Due to the dilution of the solvent, a lesser number of solvent particles are present on the surface of the solution. The surface of the solution acts as an interface between the vapor phase above it and the solution in the liquid phase. As a result of the increase in solute concentration, the solvent does not escape into the vapor phase, and this decreases the vapor pressure of the solvent.

Using solvation energy
The solvation of the solute in the solvent requires energy. Energy is expended in creation of a cavity and separation of solute particle from the bulk. These are not spontaneous processes. This expense of energy reduces the amount of energy available to the solvent particles to transform into a gas. Since fewer particles receive energy energy equivalent to their enthalpy of vaporization, the vapor pressure decreases.

Formula
For an ideal solution, the equilibrium vapor pressure is given by Raoult's law as $$p = p^\star_Ax_A+p^\star_Bx_B+ \cdots,$$ where $$p_i^\star$$ is the vapor pressure of the pure component ( $$i$$ = A, B, ...) and $$x_i$$ is the mole fraction of the component in the solution.

For a solution with a solvent (A) and one non-volatile solute (B), $$p^\star_B=0 $$ and $$p=p^\star_Ax_A$$.

The vapor pressure lowering relative to pure solvent is $$\Delta p=p^\star_A-p=p^\star_A(1-x_A)=p^\star_Ax_B$$, which is proportional to the mole fraction of solute.