At 63.5 °C, the vapor pressure of H₂O is 175 torr, and that of ethanol (C₂H₅OH) is 400 torr. A solution is made by mixing equal masses of H₂O and C₂H₅OH. (b) Assuming ideal solution behavior, what is the vapor pressure of the solution at 63.5 °C?

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of particles to escape from the liquid phase into the vapor phase. The higher the vapor pressure, the more volatile the substance. In this question, the vapor pressures of pure water and ethanol at 63.5 °C are provided, which are essential for calculating the vapor pressure of the solution.

Raoult's Law states that the vapor pressure of a solvent in a solution is equal to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution. This law applies to ideal solutions, where interactions between different molecules are similar to those between like molecules. In this scenario, Raoult's Law will be used to determine the vapor pressure of the mixed solution of water and ethanol.

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components in the mixture. It is a crucial factor in Raoult's Law, as it helps to quantify the proportion of each component in the solution. In this case, calculating the mole fractions of water and ethanol will be necessary to find the overall vapor pressure of the solution.