Question

Mrs. Gussman is using a calorimeter to find the enthalpy of fusion of a substance. The calorimeter contains 330 g of water at 31°C. A sample of the substance with a mass of 115 grams is placed into the calorimeter. Once the substance has completely dissolved, the temperature of the water inside the calorimeter is 27.4°C. Recall that the specific heat of water is 4.18 J/g-°C. What is the enthalpy of fusion (Hf) of this sample in joules per gram? For full credit, show all steps of your work.The question is also in the image since some of the symbols arent in this question

Answer 1

1) Heat absorbed by water

$q=mc\Delta T$

q= heat absorbed

m= mass (grams)

c=specific heat of water is 4.18 J/g-°C

ΔT= final temperature - initial temperature

2) Plug in known values

$q=(330gH_2O)(4.18\frac{J}{gºC})(31ºC-27.4ºC)=4965.84J$

3) Heat transferred.

Heat absorbed by water is the heat released by the sample.

4) Heat transfer by sample

$q=m\cdot\Delta Hf$

q= heat transfer

m= mass (grams)

ΔHf=enthalpy of fusion

5) Plug in known values and solve for ΔHf.

$4965.84J=(115g)(\Delta Hf)$$\frac{4965.84J}{115g}=\frac{(115g)(\Delta Hf)}{115g}$$\frac{4965.84J}{115g}=\Delta Hf$$\Delta Hf=\frac{4965.84J}{115g}=43.18\frac{J}{g}$

The enthalpy of fusion of the sample is 43.18J/g.