Question about phase change calorimetry! Help

Question

Hello, so we've recently conducted a calorimetry experiment wherein we had to mimic an isolated system by melting ice cubes in hot water.

The questions are:

1. Calculate the heat exchanged in the system
2. And from that equation, calculate the initial temperature of the ice.

and the values I used are:

mass of water = 99.24 g

mass of ice = 25.26 g

initial temperature of water = 61.2

final temperature of resulting solution = 31.6 C

I don't know how to get the heat exchanged in the system since the initial temperature of the ice was unknown but when I solved for the initial temperature of the ice, I got -37 C ): Is this correct? But how should I compute for the heat exchanged in the system?

The formula I used to get the second answer is -Qwater = Qice wherein q ice is the sum of the q needed to raise the temperature of ice + latent heat of fusion + the q of the water melted from the ice.

Answer 1

The heat exchanged by the system is simply the heat lost by the water in going from 61.2º to 31.6º.

I don't get -37º for the initial temperature of the ice. I get -4.9ºC. Here is how I arrive at that value. Please check my math, however.

heat lost by water = heat gained by ice

heat lost by water = mass x C x ∆T = (99.24 g)(4.184 J/gº)(29.6º) = 12,291 J

This is also the heat gained by the ice.

heat gained by ice = mass x ∆H_fusion + mass x C_H2O x T_f - T_i

12,291 J = (25.26 g)(334 J/g) + (25.26 g)(4.184 J/gº)(31.6º - T_i)

12,291 = 8437 + 3340 - 105.7 T_i

514 = -105.7 T_i

T_i = - 4.9ºC