Final answer:
To calculate the molality of the toluene/benzene solution, we first need to determine the number of moles of toluene and benzene in the solution. The mole fraction of toluene is given as 0.100, which can be used to calculate the moles of toluene. The molality of the solution is then calculated by dividing the moles of toluene by the mass of the solvent in kilograms.
Step-by-step explanation:
The molality of a solution is defined as the number of moles of solute divided by the mass of the solvent in kilograms. To calculate the molality of the toluene/benzene solution, we first need to determine the number of moles of toluene and benzene in the solution. The mole fraction of toluene (Xtoluene) is given as 0.100, which means that the moles of toluene divided by the total moles of both toluene and benzene is equal to 0.100.
The mole fraction of toluene can be calculated using the formula: Xtoluene = moles of toluene / (moles of toluene + moles of benzene). Rearranging the formula, we have moles of toluene = Xtoluene × (moles of toluene + moles of benzene). Since we know the mole fraction of toluene is 0.100, we can substitute the value and solve for moles of toluene.
The molality of the solution is then the moles of toluene divided by the mass of the solvent in kilograms. The mass of the solvent can be calculated using the formula: mass of solvent = volume of solvent × density of solvent. Since we are given the volumes of toluene (100.0 mL) and benzene (300.0 mL) and their densities (0.867 g/mL and 0.874 g/mL, respectively), we can calculate the masses of toluene and benzene separately and then sum them up to obtain the mass of the solvent in grams. We then convert the mass of the solvent in grams to kilograms and divide the moles of toluene by this mass to find the molality of the solution.