# How to Calculate Heat Removal in Sulfuric Acid Production

• chem_is_lovex
In summary, the gas must be cooled to 700K before it goes to the second converter in order to prevent the heat of reaction from releasing too much energy into the system.
chem_is_lovex
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 :)

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.

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

To calculate the heat removal in sulfuric acid production, we need to use the principles of thermodynamics and heat transfer. The process of sulfuric acid production involves several steps, including oxidation of sulfur to SO2, further oxidation of SO2 to SO3, and absorption of SO3 in dilute H2SO4 to form concentrated H2SO4. In this process, heat is generated as a byproduct of the chemical reactions. This heat needs to be removed in order to maintain the desired temperature for the reactions to occur.

To calculate the heat removal, we first need to determine the amount of heat generated by the reactions. This can be done by calculating the enthalpy change for each reaction using the standard heat of formation values provided in the data. The enthalpy change for the first reaction (SO2 + ½ O2 → SO3) can be calculated as follows:

ΔH = (-395.18 kJ/gmol) - (-296.9 kJ/gmol) = -98.28 kJ/gmol

Since only 75% of the entering SO2 reacts in the first converter, the heat generated by this reaction per kg mol of gases entering the process is:

Q1 = (-98.28 kJ/gmol) x (0.75) = -73.71 kJ/gmol

Next, we need to determine the heat capacity of the gases in the entering stream. This can be calculated using the given heat capacity equations for N2, O2, SO2, and SO3 at the given temperature range. Once we have the heat capacity, we can calculate the change in temperature of the gases as they go through the first converter using the following equation:

Q1 = mCpΔT

Where:
Q1 = heat generated by the reaction
m = mass of gases
Cp = heat capacity of gases
ΔT = change in temperature

Rearranging the equation, we get:

ΔT = Q1 / (mCp)

Substituting the values, we get:

ΔT = (-73.71 kJ/gmol) / (1 kg mol) x (0.090 x 29.00 + 0.095 x 29.10 + 0.815 x 38.91) = -0.72oC

This means that the temperature of the gases will decrease by 0.72oC as they

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