Question

Pure benze freeze at 5.5°C and boils at 80.1°C. What is the boiling point of a solution consisting of cyclohexane(C6H12)dissolved in benzene if the freezing point of this solution is 0.0°C?

a) 82.79°C
b) 79.75°C
c) 83.62°C
d) 78.40°C

Answer 1

The boiling point of the cyclohexane and benzene solution is calculated by finding the molality from the provided freezing point depression, and then using it along with the ebullioscopic constant of benzene to determine the boiling point elevation. The final boiling point is the sum of the elevation and the boiling point of pure benzene, giving an answer close to 82.79°C.Answer is option (a).

Step-by-step explanation:

To determine the boiling point of the solution of cyclohexane in benzene, we can use the colligative property known as boiling point elevation.

The formula to calculate the change in boiling point (ΔTb) is ΔTb = i × Kb × m, where 'i' is the van't Hoff factor (which is 1 for non-electrolytes like cyclohexane), 'Kb' is the ebullioscopic constant of benzene (2.53°C/m, not provided in the question data but is necessary for the calculation), and 'm' is the molality of the solution.

First, we calculate the change in freezing point depression (ΔTf) to find the molality because freezing point depression data is provided.

ΔTf = T(f pure solvent) - T(f solution) = 5.5°C - 0°C = 5.5°C

Using the freezing point depression constant of benzene (Kf = 5.12°C/m) and rearranging the formula ΔTf = Kf × m, we can find the molality (m).

m = ΔTf / Kf = 5.5°C / 5.12°C/m = 1.0742m

Now, we use the molality to find the boiling point elevation.

ΔTb = i × Kb × m = 1 × 2.53°C/m × 1.0742m = 2.72°C

Add ΔTb to the normal boiling point of benzene to find the boiling point of the solution.

Boiling point of solution = 80.1°C + 2.72°C = 82.82°C

Thus, the closest answer to our calculated value is (a) 82.79°C, which would be the expected boiling point of the cyclohexane and benzene solution.