Question

A solution containing 0.750g of an unknown substance in 30.0g of cyclohexane freezes at 3.1°C. What is the molar mass of the unknown substance?

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Answer 1

To find the molar mass of an unknown substance using freezing point depression, calculate the freezing point depression, then the molality, followed by the moles of solute, and finally divide the mass of the solute by moles to get the molar mass.

Step-by-step explanation:

To determine the molar mass of an unknown substance using freezing point depression, we apply the formula ΔTf = Kf * m, where ΔTf is the freezing point depression, Kf is the freezing point depression constant for the solvent, and m is the molality of the solution. To find the molality, we first need the number of moles of solute, which we get by dividing the mass of the solute by its molar mass. We then divide the moles by the mass of the solvent in kilograms to obtain molality. Lastly, we rearrange the formula to solve for molar mass (M = mass of solute / (molality * mass of solvent)).

Here's the step-by-step solution for the given problem:

1. Calculate the freezing point depression (ΔTf), which is the difference between the freezing point of pure cyclohexane and the freezing point of the solution.
2. Use ΔTf and the known freezing point depression constant (Kf) for cyclohexane to calculate the molality (m) of the solution.
3. Calculate the moles of solute using the molality and the mass of the solvent (in kg).
4. Finally, calculate the molar mass of the solute by dividing its mass (in grams) by the number of moles calculated in the previous step.