Can you help me with this phase change thermochemistry problem?

Question

How do I calculate how much heat energy is required to hear a 150g sample of ice initially At -14°C to 30°C?.

 

I know that I am supposed to use the equation q=mcΔT at some point, but I am not quite sure what else I need to do since there is a phase-change

Answer 1

For these problems, it is best to work in step/stages.  Each temperature change, and each phase change should be done separately.  So, in this problem you have a 150 g mass (this will be the same for all calculations), and you are taking it from solid ice at -14ºC to 30ºC.  This will require 3 separate steps:

(1) taking solid ice from -14º to 0º

(2) melting the ice at 0º (a phase change).  Remember that phase changes do NOT have a ∆T associated with them)

(3) taking the liquid water from 0ºC to 30ºC

 

Now, for the calculations using q = mC∆T and/or q = m∆H

(1) q = mC∆T 

q = (150 g)(2.09 J/g/deg)(14 deg) = 4389 J  (2.09 is the value I have for C_ice)

(2) q = m∆H_fus

q = (150 g)(334 J/g) = 50,100 J

(3) q = mC∆T

q = (150 g)(4.184 J/g/deg)(30 deg)

q = 18,828 J

 

Then just add up all of the joules and convert to kJ if needed.

Total heat = 73,317 J = 73.3 kJ