At \(25^{\circ} \mathrm{C}\) the vapor pressures of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\) are 93.4 and 26.9 torr, respectively. A solution made by mixing \(35.0 \mathrm{~g}\) of benzene and \(65.0 \mathrm{~g}\) of toluene is prepared. What is the vapor pressure of this solution?

Raoult's Law is a fundamental principle of physical chemistry and is pivotal when determining the vapor pressure of a solution. It states that the partial vapor pressure of each component in an ideal solution is directly proportional to its mole fraction. In more accessible terms, Raoult's Law tells us that if you have a mixture of liquids, each contributes to the total vapor pressure based on how much of it is present compared to the whole mixture.

To apply Raoult's Law, simply multiply the pure vapor pressure of each component by its mole fraction within the solution. This calculation will give you the partial vapor pressure contributed by each component. By adding these partial pressures together, you obtain the total vapor pressure of the solution. This law is hugely beneficial as it allows for the prediction of a solution's behaviors solely based on its components without needing complicated experiments.

When forming a solution, understanding the composition is crucial, and this is where the concept of mole fraction comes into play. The mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a particular substance to the total number of moles of all substances in the mixture.

You find the mole fraction by dividing the moles of one substance by the sum of moles of all substances. For example, in a binary mixture with two substances, A and B, the mole fractions would be calculated as follows:

• For A: `X_A = n_A / (n_A + n_B)`
• For B: `X_B = n_B / (n_A + n_B)`

Ensuring accuracy in this step is key to correct vapor pressure calculations, as the mole fraction is a variable in Raoult's Law.

Colligative properties are those properties of a solution that depend on the number of particles dissolved in it, not on the nature of the particles themselves. They are unique in that they offer insight into the solute without requiring knowledge about its chemical identity. Four key colligative properties exist: boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

Understanding these properties allows scientists and engineers to manipulate solutions to achieve desired outcomes, such as antifreeze in a car radiator preventing the coolant from freezing. In the context of vapor pressure, Raoult’s law helps predict how the vapor pressure will change upon adding a solute to a solvent. The presence of the solute causes a lowering of the vapor pressure because the solute molecules occupy space at the surface of the liquid, where evaporation occurs, making it more difficult for solvent molecules to escape into the gaseous phase.

Partial vapor pressure is related to Raoult's Law and is crucial for understanding the behavior of solutions. It represents the pressure exerted by a component in a mixture's vapor phase when that component is in equilibrium with its liquid phase in a closed system. Each substance in a mixture contributes to the total vapor pressure based on its own partial pressure.

Imagine a room with a mix of different scents from various perfumes. Each scent contributes to the overall smell of the room, akin to how in a mixture, each component's vapor contributes to the total vapor pressure. Calculating the partial vapor pressure involves determining the mole fraction and knowing the pure vapor pressure of the component. By multiplying these two values, as outlined in Raoult's Law, we can find how much one substance contributes to the overall pressure. Accurately calculating this prevents errors in determining the solution's complete vapor pressure.