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Working with solutions of ethylene bromide and propylene bromide, Raoult§ noticed that the vapor pressures of the components in a solution were proportional to the mole fractions of those components:

(3.8)

Figure 3.4 Vapor pressure of water and dioxane in a water–dioxane mixture showing deviations from ideal mixing. Shaded areas are areas where Raoult's law (dashed lines). Henry's law slopes are shown as dot-dashed lines. After Nordstrom and Munoz (1986).

where P_i is the vapor pressure of component i above the solution, X_i is the mole fraction of i in solution, and is the vapor pressure of pure i under standard conditions. Assuming the partial pressures are additive and the sum of all the partial pressures is equal to the total gas pressure (ΣP_i = P_total):

(3.9)

Thus, partial pressures are proportional to their mole fractions. This is the definition of the partial pressure of the i^th gas in a mixture.

Raoult's law holds only for ideal solutions, that is, substances where there are no intermolecular forces. It also holds to a good approximation where the forces between like molecules are the same as between different molecules. The two components Raoult was working with were very similar chemically, so that this condition held, and the solution was nearly ideal. As you might guess, not all solutions are ideal. Figure 3.4 shows the variations of partial pressures above a mixture of water and dioxane. Significant deviations from Raoult's law are the rule except where X_i approaches 1.