Boiling Point Elevation:

Boiling point elevation is the phenomenon where the boiling point of a liquid is increased when another compound, such as a solute, is added to it. The boiling point elevation is directly proportional to the molality of the solute.

Boiling Point Elevation Constant:

The boiling point elevation constant is a proportionality constant that relates the boiling point elevation of a solvent to the molality of the solute. The boiling point elevation constant is specific to each solvent and is constant at a given temperature.

Enthalpy of Vaporization:

The enthalpy of vaporization is the amount of energy required to vaporize one mole of a liquid at its boiling point. The enthalpy of vaporization is a measure of the strength of the intermolecular forces between the molecules in the liquid.

Calculation:

Given, boiling point elevation constant for toluene = 3.32 K kg mol^-1
Normal boiling point of toluene = 110.7°C

We know that the boiling point elevation is given by the formula:

ΔTb = Kb × m

Where ΔTb is the boiling point elevation, Kb is the boiling point elevation constant, and m is the molality of the solute.

Also, we know that the molality of the solute is given by the formula:

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

In this case, the solute is not given, so we assume that we are adding one mole of solute to one kg of solvent. Therefore, the molality of the solute is 1 mol kg^-1.

Substituting the values in the formula for boiling point elevation, we get:

ΔTb = 3.32 K kg mol^-1 × 1 mol kg^-1 = 3.32 K

The boiling point elevation is the difference between the normal boiling point and the new boiling point. Therefore, the new boiling point of toluene is:

New boiling point = Normal boiling point + ΔTb
= 110.7°C + 3.32 K
= 113.02°C

We know that the enthalpy of vaporization is given by the Clausius-Clapeyron equation:

ΔHvap = -R × T × ln(P2/P1)

Where ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature in Kelvin, and P1 and P2 are the vapor pressures of the liquid at two different temperatures.

We can assume that the vapor pressure of toluene at its normal boiling point is 1 atm. Therefore, the vapor pressure of toluene at its new boiling point of 113.02°C can be calculated using the Antoine equation:

log10(P) = A - (B / (T + C))

Where P is the vapor pressure in mmHg, T is the temperature in Celsius, and A, B, and C are constants specific to the compound.

For toluene, the constants are:

A = 6.90565
B = 1211.033
C = 220.790

Substituting the values, we get:

log10(P) = 6.90565 - (1211.033 / (113.02 + 220.790))
= 6.90565 - 4.