## Energy balance question

This was a question from one of my tutes earlier in the semester, and now that I'm revising for an exam I can't seem to remember how to do it.
If anyone can help that would be great!

Sulfuric acid is a major bulk chemical used in a wide variety of industries. After sulfur is
oxidized to SO2, the SO2 is further oxidized in the converters (reactors) to SO3
SO2 (g) + ½ O2 (g) + SO3 (g)
and the SO3 is absorbed in dilute H2SO4 to form concentrated H2SO4
In the first converter the entering gases at 400K and 1 atm are composed of 9.0% SO2, 9.5%
O2, and 81.5% N2. Only 75% of the entering SO2 reacts on going through the first converter.
If the maximum temperature of the gas before going to the next converter (where the reaction
is completed) can be 700K, how much heat must be removed from the gas before it goes to
the second converter per kg mol of gases entering the process?

Data:
Heat capacities of gases in J/gmol oC. Temperature in oC.
N2: 29.00 + 0.2199 x 10-2 T + 0.5732 x 10-5 T2
O2: 29.10 + 1.158 x 10-2 T - 0.6076 x 10-5 T2
SO2: 38.91 + 3.904 x 10-2 T – 3.104 x 10-5 T2
SO3: 48.50 + 9.188 x 10-2 T – 8.540 x 10-5 T2
Standard heat of formation (kJ/gmol):
SO2: -296.9 kJ/gmol
SO3: -395.18 kJ/gmol

thanks a lot :)
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 I don't know if it's worth answering at this point, but you have to find the enthalpy of reaction (the difference between the heats of formation of reactants and products). This is the amount of energy that will be expelled into the system. Divide this by the system heat capacity to determine the temperature change, and the necessary level of cooling.
 Based on the 75% conversion of SO2, you can calculate the total amount of heat liberated by the reaction (per kg mol of gas entering; you will need to calculate the heat of reaction using the heat of formation data you have been given). You can also work out exactly what the composition of the outlet gas is by considering the 75% conversion and the stoichiometry of the reaction. Given that you know the inlet temperature, the outlet composition and the heat liberated, you can calculate (using the heat capacities of each gas) the final temperature of the mixture. It could be somewhat tedious to solve, so something like MS excel will be handy.

## Energy balance question

hey guys, thanks for answering! I managed to do it myself though, and I did it the way you guys said :)