Verified answer

This question has four parts. The first part is the melting of solid SO2 without changing its temperature. The second part is warming up liquid SO2 up to its boiling point. The third part is vaporizing liquid sulfur dioxide at its boiling point. The fourth part is warming up SO2 gas from its boiling point to 60 degrees Celsius. Each part requires a different equation to calculate the required heat. At the end you should add up the heat values from each part to get the final answer.

Part I: Melting sulfur dioxide at its melting point of -73 degrees Celsius.

Since the heat of fusion is given in kJ/mol, we should convert 2.205 kg of sulfur dioxide to moles of sulfur dioxide:

[(2.205 kg)/1][(1,000 g)/(1 kg)][(1 mol)/(32.06 g)] = 68.78 mol of SO2

heat = moles x heat of fusion

heat = (68.78 mol)(8,619 J/mol)

heat = 592,814.82 J or 592,800 J to four significant figures

Part II: Warming liquid sulfur dioxide from its melting point to its boiling point.

The melting point temperature is given as -73 degrees Celsius, and its boiling point temperature is 10 degrees Celsius. The change in temperature is therefore 83 degrees Celsius (or K).

heat = mass x specific heat capacity x change in temperature

heat = (2,405 g)(0.995 J/g.K)(83 K)

heat = 198,616.92 J or 198,600 J to four significant figures as before

This figure should probably be reduced to two significant figures, since the temperature only has two significant figures. In that case the answer should be more like 200,000 J.

Part III: Vaporizing the liquid sulfur dioxide at its boiling point of 10 degrees Celsius.

heat = moles x heat of vaporization

heat = (68.78 mol)(25,730 J/mol)

heat = 1,769,709.4 J or 1,770,000 J to four significant figures

Part IV: Warming up sulfur dioxide gas from its boiling point to 60 degrees Celsius.

Since sulfur dioxide boils at 10 degrees Celsius, and its final temperature is 60 degrees Celsius, the change in temperature will be 50 degrees Celsius of Kelvin.

heat = mass x specific heat capacity x change in temperature

heat = (2,405 g)(0.622 J/g.K)(50 K)

heat = 74,795.5 J of 74,800 J to four significant figures as before, even though it looks like the temperature here only has one significant figure. Check with your teacher about that.

Finally need to add all the Joules of heat from each part to get the final answer:

592,800 J 198,600 J 1,770,000 J 74,800 J = 2,636,200 J

Note: These figures probably should be put in scientific notation to show that they are done to four significant figures, not three, as the last two values appear.