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Chapter 10: Problem 110

A solution is prepared by dissolving 52.3 g cesium chloride in \(60.0 \mathrm{g}\) water. The volume of the solution is \(63.3 \mathrm{mL}\). Calculate the mass percent, molarity, molality, and mole fraction of the CsCl solution.

Short Answer

Expert verified
The mass percent of the cesium chloride solution is 46.56%, the molarity is 4.906 mol/L, the molality is 5.173 mol/kg, and the mole fraction of CsCl is 0.0852.

Step by step solution

01

Find the mass of the solution

To find the mass of the solution, add the mass of cesium chloride and mass of water. Mass of cesium chloride (CsCl) = 52.3 g Mass of water (H2O) = 60.0 g Mass of solution = mass of CsCl + mass of H2O = 52.3 g + 60.0 g = 112.3 g
02

Calculate the mass percent

Mass percent is calculated by dividing the mass of the solute (CsCl) by the mass of the solution and multiplying by 100 to get the percentage. Mass percent = (mass of CsCl / mass of solution) * 100 Mass percent = (52.3 g / 112.3 g) * 100 = 46.56 %
03

Calculate the molarity

First, find the moles of CsCl using its molar mass (Cs = 132.9 g/mol, Cl = 35.45 g/mol). Then, convert the volume of the solution into liters. Finally, we can calculate the molarity by dividing the moles of CsCl by the volume of the solution in liters. Molar mass of CsCl = 132.9 + 35.45 = 168.35 g/mol Moles of CsCl = 52.3 g / 168.35 g/mol ≈ 0.3104 mol Volume of solution = 63.3 mL = 0.0633 L Molarity = moles of CsCl / volume of solution (L) Molarity = 0.3104 mol / 0.0633 L ≈ 4.906 mol/L
04

Calculate the molality

Molality is the ratio of moles of solute (CsCl) to the mass of solvent (water) in kilograms. Mass of water in kg = 60 g / 1000 = 0.06 kg Molality = moles of CsCl / mass of solvent (kg) Molality = 0.3104 mol / 0.06 kg ≈ 5.173 mol/kg
05

Calculate the mole fraction

First, find the moles of water using its molar mass (18.015 g/mol). Then, calculate the total moles in the solution. Finally, divide the moles of CsCl by the total moles in the solution to find the mole fraction. Molar mass of water (H2O) = 18.015 g/mol Moles of water = 60 g / 18.015 g/mol ≈ 3.331 mol Total moles = moles of CsCl + moles of water = 0.3104 mol + 3.331 mol ≈ 3.6414 mol Mole fraction of CsCl = moles of CsCl / total moles = 0.3104 mol / 3.6414 mol ≈ 0.0852 Summary: Mass percent of CsCl = 46.56 % Molarity of CsCl solution = 4.906 mol/L Molality of CsCl solution = 5.173 mol/kg Mole fraction of CsCl = 0.0852

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