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 0.161 g of an unknown nonelectrolyte solute and 5.818 g of cyclohexane was 3.98°C. What is the molar mass of the unknown nonelectrolyte solute?

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To determine the molar mass of the unknown solute, we can use the equation:

ΔT = Kf * m

where ΔT is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution (moles of solute per kilogram of solvent).

First, let's calculate the molality of the solution:

m = (moles of solute) / (mass of solvent in kg)

Given that the mass of cyclohexane is 5.818 g and the molar mass of cyclohexane is 84.16 g/mol, we can convert the mass to kilograms:

mass of cyclohexane (kg) = 5.818 g / 1000 = 0.005818 kg

Next, let's find the moles of cyclohexane:

moles cyclohexane = (mass of cyclohexane) / (molar mass of cyclohexane)

moles cyclohexane = 0.005818 kg / 84.16 g/mol ≈ 0.00006909 mol

Now, we can calculate the molality:

m = (moles of solute) / (mass of solvent in kg)

0.161 g of solute is equivalent to 0.161 g / Unknown solute molar mass.

Let's use "Molar mass of unknown solute" as the variable for the unknown solute molar mass.

m = (0.161 g / Molar mass of unknown solute) / 0.005818 kg

Simplifying, we get:

m = (0.161 / Molar mass of unknown solute) / 0.005818

Next, let's calculate the change in freezing point (ΔT):

ΔT = freezing point of pure solvent - freezing point of solution

ΔT = 6.60°C - 3.98°C

Now, substitute the known values into the equation ΔT = Kf * m:

ΔT = 20.00°C/m * [(0.161 / Molar mass of unknown solute) / 0.005818]

Simplifying further:

2.62 = (20.00°C/m) * [(0.161 / Molar mass of unknown solute) / 0.005818]

Now, isolate the variable Molar mass of unknown solute:

Molar mass of unknown solute = (0.161 / 2.62) / (20.00°C/m / 0.005818)

Calculating this expression gives the molar mass of the unknown solute.