A 108 mL gas sample has a mass of 77.96 mg at a pressure of 1140 mmHg and a temperature of 183 °C. Assume ideal gas behavior and a completely insulated system, and please don’t forget units with your answers.

Question

The system is cooled. Calculate the amount of heat that will be released by the system if all of the gas at 125 ºC transforms into liquid water at 59.0 ºC.
(The heat of vaporization of water at 100.0 ºC is 40.7 kJ/mol, and the heat of fusion of water at 0.0 ºC is 6.02 kJ/mol.)

Answer 1

Supposing all the "gas" is water vapor.

The source below gives the specific heat of water vapor and liquid water:
(2.000 J/(g·°C) x ((0.07796 g) x (125 ºC - 100 ºC) = 3.898 J from cooling the vapor to 100 ºC

(0.07796 g H2O) / (18.01532 g H2O/mol) = 0.00432743 mol H2O
(40.7 kJ/mol) x (0.00432743 mol) = 0.1761 kJ = 176.1 J from condensing the vapor

(4.184 J/(g·°C)) x (0.07796 g H2O) x (100 ºC - 59.0 ºC) = 13.37 J from cooling the liquid water to 59.0 ºC

3.898 J + 176.1 J + 13.37 J = 193.4 J total

Answer 2

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