From the data below, calculate the total heat (in J) needed to convert 0.816 mol of gaseous ethanol at 300.0°C and 1 atm to liquid ethanol at 25.0°C and 1 atm:

Question

b.p. at 78.d degrees C

cgas: 1.43 J/g^. degrees C

Delta Hvap: 40.5 kJ/mol

cliquid: 2.45 J/g^. degrees C

Answer 1

Will heat be needed to convert a gas to a liquid, or will heat be evolved in such a process? Think about it!

Step 1: reduce temperature of gaseous ethanol from 300ºC to gaseous ethanol at 78ºC (the boiling point)

q = mC∆T = (0.816 mol)(46 g / mol)(1.43 J/gº)(222º) = 8333 J

Step 2: Convert gaseous ethanol at 78ºC to liquid ethanol at 78ºC (phase change; not change in temp)

q = m∆Hvap = (0.816 mol)(40.5 kJ/mol) = 33.048 kJ = 33,048 J

Step 3: reduce temperature of liquid ethanol at 78ºC to liquid ethanol at 25ºC

q = mC∆T = (0.816 mol)(46 g / mol)(2.45 J/gº)(53º) = 91.9 J

Sum all the energies (joules) to get...

8333 J + 33,048 J + 92 J = 41,473 J