Question

How much energy (in kilojoules) is released when 30.5g of ethanol vapor at 97.5?C is cooled to -16.5?C? Ethanol has mp = -114.5 ?C, bp = 78.4 ?C, ?Hvap = 38.56 kJ/mol and ?Hfusion = 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

Hi

heat capacity of ethanol is 113 joules per mole per degree Kelvin. This means that ethanol loses 113 joules for every degree it cools if you're talking about one mole. If you've got two moles it would be 2 x 113 joules or 216 and if it were less than one mole it would be less than 113 joules; so the first thing you must find is how many moles you have. Well ethanol (C2H5OH) has a molecular weight of 46 grams. since you have 30.5 g, you have less than one mole and we've got to calculate what fraction of a mole you have:

30.5g x 1 mole/46g = 0.663 moles

Okay, now how many degrees did it drop in temperature? Well it went from 97.5 degrees to -16.5. That's 106 degrees. Since kelvin degrees and Celsius degrees are the same size, the change in temperature is the same if we use either scale. Now if we had one mole of ethanol, the answer would simply be 114 degrees x 113 joules / mole degree x 1 mole. Since we only have 0.663 moles, the answer is 114 x 113 /0.663 = 18,066 joules. Since they want the answer in Kilojoules it would be 19.429 kJ.
Since you have a liquid to begin with and you're not turning it into a liquid from a gas or a solid from a liquid (you're not cooling it enough), you don't need to worry about the heat of vaporization or fusion