How much heat in kilojoules

Question

How much heat in kilojoules is evolved in converting 1.00 mol of steam at 150 C to ice at -70.0 C? The heat capacity of steam is 1.84 J/gC and that of ice is 2.09 J/gC.Remember that if heat is leaving the system, then q is a negative number and if heat is entering the system, then q is a positive number.

q= ? kJ

Answer 1

step 1: heat evolved converting 1.00 mol steam @ 150C to steam at 100C:

q = mC∆T = (1.00 mol x 18 g/mol)(1.84 J/gº)(50º) = 1656 J

step 2: heat evolved converting 1.00 mol steam at 100C to liquid at 100C:

phase transition, no change in temperature.

q = m x ∆Hvap = 18 g x 2260 J/g = 40,680 J

step 3: heat evolved converting 1.00 mol liquid water @ 100C to liquid at 0C:

q = mC∆T= (18 g)(4.184 J/gº)(100º) = 7531 J

step 4: heat evolved converting 1.00 mol liquid at 0º to ice at 0º:

phase transition, not change in temperature

q = m x ∆Hfusion = 18 g x 334 J/g = 6012 J

step 5: heat evolved converting 1.00 mol ice at 0º to ice at -70º:

q = mC∆T = (18 g)(2.09 J/gº)(75º) = 108 J

step 6: add up all the heat values:

1656 + 40,680 + 7531 + 6012 + 108 = 55,987 J = 55.987 kJ = 56.0 kJ (3 sig. figs.)