calculating energy needed to raise temperature of water

Question

calculate the energy (in kj) required to raise the temperature of 0.832 grams of water from -15.75 degree celsius to 21.84 degree celsuis.

the answer choices were:

0.0274

2.63

104

0.381

0.305

when i did the problem i got 130.7 which is not one of the answer choices, so if someone can help me understand how to get the correct answer, i would be so thankful!

Answer 1

When doing these types of problems, you must look at the phases of the material. For example, water at -15.75 degrees (where it begins in this problem) is ICE. So, you must first raise the temp to 0º, then you must MELT the ice at 0º (phase change), then you must heat the liquid water to the final temp of 21.84º. So, let's take these 1 step at a time.

Heat to raise temp of 0.832 g of ICE from - 15.75º to 0º:

q = mC∆T = (0.832 g)(2.09 J/gº)(15.75º) = 27.39 J (looked up C for ice and found 2.09 J/gº)

Heat to melt 0.832 g if ice at 0º:

q = m∆H_fusion = (0.832 g)(334 J/g) = 277.9 J (looked up ∆H_fusion)

Heat to raise temp of 0.832 g of water from 0º t0 21.84º:

q = mC∆T = (0.832 g)(4.184 J/gº)(21.84º) = 76.03 J

Add them all up and convert to kJ:

27.39 J = 277.9 J + 76.03 J = 381 J = 0.38 kJ