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Vapour pressure is a key concept in understanding how different substances behave when mixed together in a solution. It is essentially the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature. In the context of the exercise, we are given the vapor pressures of benzene before and after a solid is added. This is crucial because the vapor pressure of a liquid is influenced by the presence of a non-volatile solute, which is the solid added to benzene in our example.

When a non-volatile substance is dissolved in a volatile solvent like benzene, the vapor pressure of the solution is lower than that of the pure solvent. This happens because the solute molecules occupy space at the surface, reducing the number of solvent molecules that can escape into the vapor phase. The reduction in vapor pressure can be calculated using Raoult’s Law, which provides a way to determine how much the vapor pressure decreases based on the concentration of the solute.

The mole fraction is a way of expressing the concentration of a component in a mixture. It is the ratio of the number of moles of one component to the total number of moles in the solution. It is a dimensionless quantity, meaning it has no units, and it values between 0 and 1. This concept is integral to Raoult's Law, as it helps determine the influence of a solute on the solvent's vapor pressure.

In our calculation, the mole fraction of benzene was found after rearranging Raoult's Law. This value was calculated as the ratio of the vapor pressure of the solution to the vapor pressure of pure benzene: \[ X_{benzene} = \frac{600}{640} = 0.9375 \] This means that 93.75% of the moles in the solution are benzene. By understanding the mole fraction, we can work backward to find the total moles in the solution, which ultimately reveals the number of moles of the unknown solid.

Molar mass, or molecular weight, is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). Calculating molar mass is key to identifying unknown substances, as it connects the mass of a substance with the number of particles or molecules it contains.

In the exercise, we were tasked to find the molar mass of a non-volatile solid added to benzene. We accomplished this by first determining the moles of the benzene and the solid in the solution using the mole fraction. Once we knew the number of moles of the solid, we used the formula:\[ M_{solid} = \frac{m_{solid}}{n_{solid}} \]This final step directly gives us the molar mass of the solid. Plugging in the values from the original solution, we calculated:\[ M_{solid} = \frac{2.175}{0.0335} \approx 64.93 \, \text{g/mol} \]Understanding this process can help students grasp how colligative properties and compound identification work hand in hand.