In a binary ideal solution, the partial pressure of component i is given by which expression?

• A. P_i = x_i P_i°
• B. P_i = x_i P_j°
• C. P_i° = x_i P_i
• D. P_i = x_j P_i°

Answer: (A)

The key concept is Raoult's law for ideal solutions: each component contributes to the vapor pressure independently, so the partial pressure of a component i equals its mole fraction in the liquid times its pure-component vapor pressure at the same temperature. Thus the partial pressure is P_i = x_i P_i°, where x_i is the mole fraction of i in the liquid and P_i° is the vapor pressure of pure component i. This is why P_i = x_i P_i° is the correct expression.

Why the others aren’t right: using the other component’s vapor pressure P_j° would mix in the wrong substance, and using P_i° = x_i P_i would incorrectly imply that a pure substance’s vapor pressure depends on its liquid composition. Likewise, using the other mole fraction x_j would assign the wrong proportion to i’s partial pressure.