A solution that contains 0.500 g phenol in 12.0 g cyclohexane freezes at ¨C2.44¡ãC and boils at 81.94¡ãC. Calculate the freezing©\point depression and boiling©\point elevation constants for cyclohexane.

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moles phenol = g/molar mass
Solve for moles.

molality = moles phenol/kg solvent
Solve for molality

delta T = Kf*m
Solve for Kf

delta T = Kb*m
Solve for Kb.

3.6

To calculate the freezing-point depression and boiling-point elevation constants for cyclohexane, we need to use the formula:

ΔTf = Kf * m * i

ΔTb = Kb * m * i

Where:
ΔTf = freezing-point depression
ΔTb = boiling-point elevation
Kf = freezing-point depression constant for cyclohexane
Kb = boiling-point elevation constant for cyclohexane
m = molality of the phenol solution
i = Van't Hoff factor

First, let's calculate the molality (m) of the phenol solution:

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

Given:
Mass of phenol (solute) = 0.500 g = 0.0005 kg
Mass of cyclohexane (solvent) = 12.0 g = 0.012 kg
Molar mass of phenol = 94.11 g/mol

Moles of solute = mass of solute / molar mass of solute
Moles of solute = 0.0005 kg / 94.11 g/mol = 0.00000532 mol

Molality (m) = 0.00000532 mol / 0.012 kg = 0.00044 mol/kg

Next, we need to determine the Van't Hoff factor (i) for phenol. The Van't Hoff factor represents the number of particles the solute breaks into in the solution. Since phenol does not dissociate or ionize in the solution, i = 1.

Now, we can calculate the freezing-point depression (ΔTf) and boiling-point elevation (ΔTb) using the given data:

ΔTf = -2.44°C (freezing point) - 0°C (pure solvent)
ΔTf = -2.44°C

ΔTb = 81.94°C (boiling point) - 100°C (pure solvent)
ΔTb = -18.06°C

Finally, we can calculate the freezing-point depression constant (Kf) and boiling-point elevation constant (Kb) using the formulas:

Kf = ΔTf / (m * i)
Kb = ΔTb / (m * i)

Calculating Kf:
Kf = -2.44°C / (0.00044 mol/kg * 1)
Kf = -5554.55°C/mol

Calculating Kb:
Kb = -18.06°C / (0.00044 mol/kg * 1)
Kb = -41090.91°C/mol

Therefore, the freezing-point depression constant (Kf) for cyclohexane is -5554.55 °C/mol, and the boiling-point elevation constant (Kb) for cyclohexane is -41090.91 °C/mol.