A freezing point depression experiment was conducted using cyclohexane as the solvent. The freezing point of pure cyclohexane is 6.60°C and the freezing point depression constant is 20.00°C/m. The freezing point of a solution containing 0.135 g of an unknown nonelectrolyte solute and 5.759 g of cyclohexane was 2.14°C. What is the molar mass of the unknown nonelectrolyte solute?
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To find the molar mass of the unknown solute, we can use the equation:
ΔT = Kf * m
Where:
ΔT is the freezing point depression (difference in freezing point),
Kf is the freezing point depression constant for the solvent,
m is the molality of the solute (moles of solute per kg of solvent).
First, let's calculate the molality (m) of the solute:
Molality (m) = moles of solute / mass of solvent in kg
Given that the mass of the solute is 0.135 g and the mass of the solvent is 5.759 g, we need to convert the mass of the solvent to kg:
Mass of solvent (cyclohexane) = 5.759 g = 0.005759 kg
Now, we can calculate the molality (m):
m = 0.135 g / 0.005759 kg
m = 23.42 mol/kg
Next, we can use the freezing point depression equation to solve for the change in temperature (ΔT):
ΔT = Kf * m
ΔT = 20.00°C/m * 23.42 mol/kg
ΔT = 468.4 °C
The freezing point depression is the difference between the freezing point of the solvent and the freezing point of the solution:
ΔT = Freezing point of pure solvent - Freezing point of solution
Rearranging the equation, we can solve for the freezing point of the solution:
Freezing point of solution = Freezing point of pure solvent - ΔT
Freezing point of solution = 6.60°C - 468.4 °C
Freezing point of solution = -461.8 °C
However, a freezing point lower than the normal freezing point of cyclohexane does not make sense, indicating an error in the calculation or experimental setup. Please double-check the values given in the problem to ensure accuracy.