Question

A 110.1 gram sample of an unknown substance (MM = 189.50 g/mol) is cooled from 233.0 °C to 147.6 °C. (heat capacity of liquid = 1.62 J/g･°C; heat capacity of gas = 1.04 J/g･°C; ∆Hvap = 78.11 kJ/mol; Tb = 160.3 °C)

A. How much energy (in kJ) is absorbed/released to cool the gas?

B. How much energy (in kJ) is absorbed/released to condense the gas?

C. How much energy (in kJ) is absorbed/released to cool the liquid?

D. What is the total amount of energy that must be absorbed/released for the entire process?

Answer 1

The unknown substance is cooled from 233.0ºC to 147.6ºC. The entire process consists of the following sub-processes:

A. Cooling the gas from 233.0ºC to 160.3ºC.

B. Condensation of the gas at its boiling point, Tb = 160.3ºC.

C. Cooling the liquid from 160.3ºC to 147.6ºC.

A. Heat capacity of the gas = 1.04 J/g.ºC

Heat absorbed/released = (mass of the gas)*(heat capacity of the gas)*(change in temperature of the gas)

= (110.1 g)*(1.04 J/g.ºC)*(160.3 – 233.0)ºC

= -8324.4408 J

= (-8324.4408 J)*(1 kJ)/(1000 J)

= -8.3244408 kJ

≈ -8.32 kJ (ans)

Since the heat involved in the cooling process is negative, hence, the heat energy is released. This is a general trend; heat must be absorbed by a substance to increase its temperature and heat must be released by the substance to lower its temperature.

B. Molar mass of the substance = 189.50 g/mol.

Mol(s) of the substance corresponding to 110.1 g = (110.1 g)/(189.50 g/mol)

= 0.5810 mol.

ΔHvap = 78.11 kJ/mol

Since the gas condenses to the liquid, hence heat must be released and the heat released is given as

Heat released = (mols of the substance)*(-ΔHvap)

= (0.5810 mol)*(-78.11 kJ/mol)

= -45.38191 kJ

≈ -45.38 kJ (ans)

C. Heat capacity of the liquid = 1.62 J/g.ºC

Heat absorbed/released = (mass of the liquid)*(heat capacity of the liquid)*(change in temperature of the gas)

= (110.1 g)*(1.62 J/g.ºC)*(147.6 – 160.3)ºC

= -2265.1974 J

=(-2265.1974 J)*(1 kJ)/(1000 J)

= -2.2651974 kJ

≈ -2.26 kJ (ans)

Again, this is a cooling process; so the heat involved must be negative.

D. Total heat released in the process = [(-8.32 kJ) + (-45.38 kJ) + (-2.26 kJ)]

= -55.96 kJ

≈ -56.0 kJ (ans, correct to 3 sig. figs).