Question

How much energy (in kilojoules) is released when 22.0 g of ethanol vapor at 97.5 ∘C is cooled to -12.5 ∘C? Ethanol has mp = -114.5 ∘C, bp = 78.4 ∘C, ΔHvap = 38.56 kJ/mol and ΔHfusion = 4.60 kJ/mol. The molar heat capacity is 113 J/(K⋅mol) for the liquid and 65.7 J/(K⋅mol) for the vapor.

Answer 1

Solution.

Since the ethanol starts as a vapor, and changes into a liquid, we'll want to do its cooling as 2 separate
steps (for gas (g) and for liquid (l) state).

For the first step we find the energy to take the vapor from 97.5 to the boiling point:

Then use the negative energy of vaporation  to make the liquid:

For the next step we'll find the energy to go from the boiling point to -12.5 centigrades:

The overall heat is a sum:

As the heat is negative for a system it means energy releasing, so the system released .

Answer: