Using heat of fusion or vaporization to find the heat needed to melt or boil a substance

Question

Calculate the amount of heat needed to boil 37.6g of ethanol (CH3CH2OH), beginning from a temperature of −59.7°C. Round your answer to 3 significant digits. Also, be sure your answer contains a unit symbol. 

Answer 1

So, what is the phase of ethanol at -59.7ºC. Looking it up, I find it to be a liquid at this temperature because the freezing point is -114ºC.

Since it is a liquid at this temperature, and we want to boil it, we also need to know the specific heat of liquid ethanol, as well as the ∆Hvaporization and the boiling point, Again, looking up these values I find them to be:

specific heat (C) = 2.40 J/gº

∆Hvap = 838.3 J/g

BP = 78.2ºC

Now using all of these constants, we can approach the answer to the question.

(1) heat needed to raise 37.6 g ethanol from -59.7º to the boiling point of 78.2ºC:

q = mC∆T

q = (37.6 g)(2.40 J/gº)(137.9º) = 12,444 J

(2) heat needed to boil 37.6 g at 78.2º (phase change):

q = m∆Hvap = (37.6 g)(838.3 J/g) = 31,520 J

Total heat needed = 12,444 J + 31,520 J = 43,964 J = 43.9 kJ