Question

A calorimeter contains 500 g of water at 25°C. You place a hand warmer containing 100 g of liquid sodium acetate (NaAC) inside the calorimeter. When the sodium acetate finishes crystallizing, the temperature of the water inside the calorimeter is 32.2°C. The specific heat of water is
4.18 J/g-°C. What is the enthalpy of fusion (ΔHf) of the sodium acetate? I need to see the work and make sure its right

Answer 1

The equation we're ultimately going to be working with is:
\[ΔHn=mcΔT\]
Where:

ΔH is the enthalpy of fusion of NaAC
n is the moles of NaAC
m is the mass of water
c is the specific heat of water
ΔT is the temperature change

Heat is transferred from NaAC (left side of the equation) to the water in the calorimeter (right side of the equation). We're almost ready to sub in our numbers, we just need to find moles of NaAC by dividing mass by molar mass: 100 g / 82 g/mol = 1.22 mol.

Now we just need to sub in our numbers!

\[ΔHn=mcΔT\]\[ΔH(1.22) = 500(4.18)(32.2-25)\]\[ΔH=12334\]
Therefore the heat of fusion of NaAC is 12334 J/mol or 12.3 kJ/mol.