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? Show your work.

Answer 1

Answer:The enthalpy of fusion $(ΔH_f)$ of the sodium acetate is 12.344 kJ/mol.

Explanation:

Heat absorbed by the water: Q

Change in temperature of water,$\Delta T=32.2^oC-25^oC=7.2^oC$

Specific heat of water = 4.18 J/g°C

Mass of water = m= 500 g

$Q=500 g\times 4.18 J/g ^oC\times 7.2^oC=15,048 J$

$\Delta H_f$ is the heat energy required to melt the one mole of substance.

When 200 g of sodium acetate crystallizes it gave 15,048 Joules of heat which was absorbed by the water in calorimeter.

$NaAC(l)\rightarrow NaAC(s),\Delta H_f=?$

Moles of NaAC=$\frac{100 g}{82.03 g.mol}=1.2190 mol$

$\Delta H_f=\frac{15,048 J}{1.2190 mol}=12,344 J/mol=12.344 kJ/mol$

The enthalpy of fusion $(ΔH_f)$ of the sodium acetate is 12.344 kJ/mol.

Answer 2

The heat absorbed by the water is
Q = 500 (4.18) (32.2 - 25)
Q = 15048 J

The enthalpy of fusion of the sodium acetate is:
ΔHf = Q / m
ΔHf = 15048 / 100
ΔHf = 150.48 J/g