Question

The enthalpy of vaporization for methanol is 35.2 kJ/ mol. Methanol has a vapor pressure of 1 atm at 64.7 °C. Using the Clausius-Clapeyron equation, what is the vapor pressure for methanol at 41.9 °C?

Give your answer in atmospheres, to the third decimal point.
Question 2
3 pts
The enthalpy of vaporization for dimethyl ether is 27.5 kJ/mol. Dimethyl ether has a vapor pressure of 760 torr at 34.6 °C. Using the Clausius-Clapeyron equation, what is the vapor pressure tor methanol at 0.1 °C? Give your answer in torr, to the first decimal point.

Answer 1

To use the Clausius-Clapeyron equation, we need to know two sets of conditions for the substance in question. Let's start with question 1:

Question 1:

Given:

Enthalpy of vaporization, ΔHvap = 35.2 kJ/mol

Vapor pressure at T1 = 1 atm (or 760 torr), T1 = 64.7°C

We want to find: Vapor pressure at T2 = 41.9°C

First, we need to convert temperatures to Kelvin:

T1 = 64.7 + 273.15 = 337.85 K

T2 = 41.9 + 273.15 = 315.05 K

Now we can use the Clausius-Clapeyron equation:

ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1)

where P1 and P2 are the vapor pressures at temperatures T1 and T2, respectively, R is the gas constant (8.314 J/mol·K), and ln is the natural logarithm.

Solving for P2, we get:

P2/P1 = e^(-ΔHvap/R * (1/T2 - 1/T1))

P2 = P1 * e^(-ΔHvap/R * (1/T2 - 1/T1))

Substituting the given values, we get:

P2 = 1 atm * e^(-35.2 kJ/mol / (8.314 J/mol·K) * (1/315.05 K - 1/337.85 K))

P2 = 0.496 atm

Rounding to three decimal places, the vapor pressure of methanol at 41.9°C is 0.496 atm.

Answer: 0.496 atm

Question 2:

Given:

Enthalpy of vaporization, ΔHvap = 27.5 kJ/mol

Vapor pressure at T1 = 760 torr, T1 = 34.6°C

We want to find: Vapor pressure at T2 = 0.1°C

Converting temperatures to Kelvin:

T1 = 34.6 + 273.15 = 307.3 K

T2 = 0.1 + 273.15 = 273.25 K

Using the Clausius-Clapeyron equation:

ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1)

Solving for P2, we get:

P2/P1 = e^(-ΔHvap/R * (1/T2 - 1/T1))

P2 = P1 * e^(-ΔHvap/R * (1/T2 - 1/T1))

Substituting the given values, we get:

P2 = 760 torr * e^(-27.5 kJ/mol / (8.314 J/mol·K) * (1/273.25 K - 1/307.3 K))

P2 = 7.25 torr

Rounding to one decimal place, the vapor pressure of dimethyl ether at 0.1°C is 7.3 torr.

Answer: 7.3 torr