Question

How much energy (in kilojoules) is released when 26.5g of ethanol vapor at 86.0C is cooled to -12.0C? Ethanol has mp = -114.5C , bp = 78.4C, delta H vap = 38.56 (KJ/mol) and delta H fus = 4.60 (KJ/mol) . The molar heat capacity is 113J/(K.mol) for the liquid and 65.7 J/(K.mol) for the vapor.

Answer 1

You must calculate the heat evolved in stages, then add all of the heats together to obtain the sum. Here is the way you go about it.
q1 = heat lost in moving the vapor from the starting point to the boiling point.
q1 = mass vapor x specific heat vapor x (Tfinal-Tinitial) where Tfinal will be the boiling point and Tinitial is where you start.

q2 = heat lost in condensing the vapor at the boiling point.
q2 = mass vapor at the boiling point x delta Hvaporization.

q3 heat lost in cooling the liquid vrom the boiling point to the melting (freezing) point.
q3 = mass liquid x specific heat liquid x (Tfinal-Tinitial) where Tfinal is the melting point and Tinitial is the boiling point.

q4 = heat lost is freezing the liquid.
q4 = mass liquid x heat fusion.

q5 = heat lost in moving the temperature from the freezing point to the final T.
q5 = mass solid x specific heat solid x (Tfinal - Tinitial) where Tfinal is the final T and Tinitial is the melting point.
qtotal = q1 + .....q5.
Watch the units. I note most of the specific heats are in J or kJ/mol but the mass is in grams.