The industrial solvents chloroform (CHCl₃) and dichloromethane (CH₂Cl₂) are prepared commercially by the reaction of methane with chlorine, followed by fractional distillation of the product mixture. At 25 °C, the vapor pressure of CHCl₃ is 205 mm Hg, and the vapor pressure of CH₂Cl₂ is 415 mm Hg. What is the vapor pressure in mm Hg at 25 °C of a mixture of 15.0 g of CHCl₃ and 37.5 g of CH₂Cl₂?

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 chloroform and dichloromethane at 25 °C are essential for calculating the total vapor pressure of their mixture.

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the mixture. This principle allows us to calculate the partial vapor pressures of each component in a mixture based on their individual vapor pressures and their respective mole fractions. Applying Raoult's Law is crucial for determining the total vapor pressure of the mixture of CHCl₃ and CH₂Cl₂.

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 dimensionless quantity that helps in calculating the contributions of each component to the overall properties of the mixture, such as vapor pressure. In this problem, calculating the mole fractions of CHCl₃ and CH₂Cl₂ is necessary to apply Raoult's Law effectively.