Help with Energy of Phase Change

Question

Determine the total amount of energy in J that is released when an ice cube weighing 8.0 g warms from an initial temperature of -4.70 ∘C to its melting point of 0.00 ∘C and then melts completely. Report your answer as a number in standard notation with three significant figures. (The specific heat of ice is 2.04 J/(g⋅ ∘C) and its heat of fusion is 6.01 kJ/mol.)

I understand that you would first calculate solid ice cube to melting point so you use Q=mcdeltaT to get 76.704 J, but for the second part you would convert the 8.0 grams to moles and use Qvap=6.01 kJ/mol *0.444 = 2.668 kJ * 1000 for J and this gets me a number that isn't 3 sig figs. What am i doing wrong?

Answer 1

First, heat isn't released when the ice cube melts. Heat is ADDED (endothermic). But yes, you first determine heat needed to raise the temperature of the ice cube from -4.70º to 0º as follows:

q = mC∆T

q = (8.0 g)(2.04 J/gº)(4.70º) = 76.70 J

Now that the ice is @0º, we use q = m∆Hf to find the heat needed to melt the ice cube. We don't use heat of vaporization, but rather heat of fusion (Hf).

If you want to use 6.01 kJ/mol and 8.0 g, your answer should have only 2 sig.figs since 8.0 grams has

only 2 s.f.

8.0 g x 1 mol / 18 g = 0.444 moles

6.01 kJ/mol x 0.444 mols = 2.67 kJ = 2670 J

Total energy (in joules) = 76.7 J + 2670 J = 2746.7

If you want to round to 2 sig.figs. you would report the answer as 2700 J

If you want 3 sig.figs. you would report the answer as 2750 J