A 100g sample of ice at 0ºC is added to 150.0 mL of liquid water at 80ºC in a styrofoam cup calorimeter. (The specific heat capacity of water is 1.184 J/g•ºC, the density of water is 1.00 g/mL, and ∆Hºfus = 6.01 kJ/mol)

Question

a) Does all of the ice melt?( show work to receive credit)
b) What is the final temperature once thermal equilibrium is established?
c) How much ice remains once thermal equilibrium is established?

Answer 1

a. q1 needed to melt all of the ice
q1 = mass ice x heat fusion.

q2 = mass H2O x specific heat H2O x delta T. (and the specific heat H2O is NOT 1.184).(Consider delta T = 80 which is the maximum heat that can be released). There is more than enough to melt all of the ice. This work answers a and the conclusion answers c.
For b, just put all of this together.

q1 = heat to melt ice.
q1 = [mass ice x heat fusion]

q2 = heat to raise temperature of melted ice to final T.
q2 = mass melted ice x specific heat H2O x (Tf-Ti) (of course Ti is zero).

q3 = heat released by the 80 C water.
q3 = [mass H2O x specific heat H2O x (Tf-Ti) (Ti of course is 80.)

Now just add all of these together. The sum is zero.
q1 + q2 + q3 = 0
Substitute q1, q2 and q3 from above and solve for Tf. I estimated the value and obtain something around 20 C or so.