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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delta T = Kf*m

Substitute delta T (6.60-3.98), Kf (20.00) and solve for m = molality

m = mols/kg solvent. You know m and kg solvent (0.005818); solve for mols

mols = grams/molar mass. You know mols and grams, solve for molar mass.

To find the molar mass of the unknown nonelectrolyte solute, we can use the formula:

ΔT = Kf * m

where:
ΔT is the freezing point depression
Kf is the freezing point depression constant
m is the molality of the solution

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

molality (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 approximately 84.16 g/mol, we can calculate the moles of cyclohexane:

moles of cyclohexane = mass of cyclohexane / molar mass of cyclohexane
= 5.818 g / 84.16 g/mol
≈ 0.0692 mol

Since the molar mass of the unknown solute is unknown, we will use the symbol "M" to represent it.

Since the mass of the solute given is 0.161 g, we can calculate the moles of solute:

moles of solute = mass of solute / molar mass of solute
= 0.161 g / M mol/g
= 0.161/M mol

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

m = moles of solute / mass of solvent (in kg)
= (0.161/M) mol / (5.818 g / 1000 g/kg)
= (0.161/M) mol / 0.005818 kg
= (0.161/M) / 0.005818 mol/kg
≈ (0.161 * 1000) / (0.005818 * M) mol/kg
≈ 277.09 / M mol/kg

Now, let's use the freezing point depression equation to find the molar mass.

ΔT = Kf * m

Given that ΔT (the freezing point depression) is 6.60°C - 3.98°C = 2.62°C, and Kf (the freezing point depression constant) is 20.00°C/m, let's substitute the values:

2.62°C = 20.00°C/m * (277.09 / M) mol/kg

Simplifying the equation:
2.62°C = 5.5418 / M mol/kg°C

Cross-multiplying the equation:
2.62°C * M = 5.5418 mol/kg°C

Dividing both sides by 2.62°C:
M = 5.5418 mol/kg°C / 2.62°C
M ≈ 2.1131 mol/kg

Finally, to convert mol/kg to g/mol, we need to multiply by 1000:

M ≈ 2.1131 mol/kg * 1000 g/kg
M ≈ 2113.1 g/mol

Therefore, the molar mass of the unknown nonelectrolyte solute is approximately 2113.1 g/mol.

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

ΔT = Kf * m,

where:
- ΔT is the freezing point depression
- Kf is the freezing point depression constant
- m is the molality of the solute

First, let's calculate the moles of cyclohexane present in the solution:

moles of cyclohexane = mass of cyclohexane / molar mass of cyclohexane

mass of cyclohexane = 5.818 g (given)

The molar mass of cyclohexane is 84.16 g/mol.

moles of cyclohexane = 5.818 g / 84.16 g/mol ≈ 0.0692 mol

Next, let's calculate the molality of the solute:

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

mass of solvent = mass of cyclohexane = 5.818 g = 0.005818 kg

To find the moles of solute, we need to use the freezing point depression:

ΔT = Tf - Tfp
- ΔT is the freezing point depression (3.98°C - 6.60°C = -2.62°C = -2.62 K)
- Tf is the freezing point of the solution (3.98°C)
- Tfp is the freezing point of pure solvent (6.60°C)

Now we can calculate the molality:

molality (m) = moles of solute / mass of solvent (in kg)
-2.62 K = 20.00°C/m * m

Solving for m:

m = -2.62 K / (20.00°C/m)
m ≈ -0.131

Since molality can't be negative, we need to take the absolute value:

m ≈ 0.131

Finally, we can calculate the moles of solute:

molality (m) = moles of solute / 0.005818 kg

moles of solute = 0.131 * 0.005818 kg ≈ 0.000761 mol

Now, let's find the molar mass of the unknown nonelectrolyte solute:

molar mass = mass of solute / moles of solute

mass of solute = 0.161 g (given)

molar mass = 0.161 g / 0.000761 mol ≈ 211.51 g/mol

Therefore, the molar mass of the unknown nonelectrolyte solute is approximately 211.51 g/mol.