How to find the temperature of a reaction in reactor design?

This is a little tricky

A + B = C

A reaction is not a mixture of reactants. During a chemical reaction, for example in the above reaction, the composition of A and B would change continuously depending on the pathway of the reaction and intermediate products. These intermediate products are unknown/unpredictable products. The second problem is that a reaction can be endothermic or exothermic. This brings further complication because you have to take the sign of enthalpy change into account depending on if it is exothermic or endothermic So, Q = m Cp dt or dt = Q/ mCp is not an answer since Cp does not remain the Cp of a reactant during a reaction as explained.

How temperature of a reaction is found?

The procedure is as follows

Step by step

Refer to Gibbs free energy equation dG = dH - TdS When a reaction is feasible it's free energy change dG =0 When dH is positive the reaction is not feasible. The reaction reverses. When dH is negative the reaction is a spontaneous forward reaction. When a reaction is feasible dG =0, dH = TdS or T = dH / dS dG is the free energy change of the reaction dH is the enthalpy change of the reaction. It takes care of signs, positive or negative that is exothermic or endothermic nature of reaction dH of reaction ( this is the heat of reaction) =

(dH of products - dH of reactants) dH = (enthalpy change or heat of formation)

You have to find the enthalpy of the formation of reactants from references to get the enthalpy change dH of the product. These data are easily available on the internet. Refer to the NIST data website. dS is entropy

Find out dS in the next step.

dS of a reaction = (dS of products - dS of reactants) Entropy change dS can be positive or negative. Find out entropy change data from NIST for products and reactants to get dS So, you all data

Calculate T = dH / dS

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