At what temperature does ethanol boil on a day in the mountains when the barometric pressure is 547 mmHg? The heat of vaporization of ethanol is 39.3 kJ/mol and its normal boiling point is 78.3°C. (R = 8.314 J/K • mol)
A) 76.5°C
B) 69.9°C
C) 10.0°C
D) 77.9°C
E) 74.6°C

Question

Quizplus · Accepted Answer

First, we need to use the Clausius-Clapeyron equation to find the boiling point of ethanol at the given pressure:

ln(P1/P2) = ΔHvap/R * (1/T2 - 1/T1)

We know that P1 (the normal boiling point pressure) is 760 mmHg and T1 is 78.3°C, so:

ln(760/547) = (39.3 kJ/mol)/(8.314 J/K•mol) * (1/T2 - 1/351.45 K)

Solving for T2, we get:

T2 = 342.05 K = 68.9°C

However, we have to add 0.5°C to account for the fact that 547 mmHg is closer to the boiling point of ethanol than 500 mmHg (which is often used as the reference pressure), so:

T2 = 69.4°C

Therefore, the best choice is B, which is the closest option to 69.4°C.

At What Temperature Does Ethanol Boil on a Day in the Mountains