To make a solution, 40 g of a nonelectrolyte is dissolved into 300 g of water. The
freezing point depression of the solution is measured to be -7°C. Calculate the molar
mass of the solute.
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To make a solution, 40 g of a nonelectrolyte is dissolved into 300 g of water. The
freezing point depression of the solution is measured to be -7°C. Calculate the molar
mass of the solute.
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Given:
[tex]\text{mass of solute = 40 g}[/tex]
[tex]\text{mass of solvent = 300 g = 0.300 kg}[/tex]
[tex]\text{FP}_{solution} = -\text{7°C}[/tex]
Required:
[tex]\text{molar mass of solute}[/tex]
Solution:
Step 1: Calculate the freezing point depression.
[tex]\Delta T_{f} = \text{FP}_{solvent} - \text{FP}_{solution}[/tex]
[tex]\Delta T_{f} = \text{0°C} - (-\text{7°C})[/tex]
[tex]\Delta T_{f} = \text{7°C}[/tex]
Step 2: Calculate the molality of the solution.
[tex]\Delta T_{f} = k_{f}m[/tex]
[tex]m = \frac{\Delta T_{f}}{k_{f}}[/tex]
[tex]m = \frac{\text{7°C}}{(\text{1.86 °C/}m)}[/tex]
[tex]m = 3.7634 \: m[/tex]
Step 3: Calculate the number of moles of solute.
[tex]\text{moles of solute} = m × \text{mass of solvent}[/tex]
[tex]\text{moles of solute} = 3.7634 \: m × \text{0.300 kg}[/tex]
[tex]\text{moles of solute = 1.129 mol}[/tex]
Step 4: Calculate the molar mass of the solute.
[tex]\text{molar mass of solute} = \frac{\text{mass of solute}}{\text{moles of solute}}[/tex]
[tex]\text{molar mass of solute} = \frac{\text{40 g}}{\text{1.129 mol}}[/tex]
[tex]\boxed{\text{molar mass of solute = 35.4 g/mol}}[/tex]
[tex]\\[/tex]
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