OpenSpecEngineering

Finds the standard heat of reaction for a reaction with up to two reactants and two products, from their standard enthalpies of formation. It says whether the reaction gives off heat or takes it in. Given the heat capacity of the product stream, it also finds how far the temperature changes in an adiabatic reactor. Process engineers use it for energy balances, reactor cooling duties and first checks on runaway risk.

Equations

ΔH°_rxn = Σν_P·ΔH°_f,P − Σν_R·ΔH°_f,R

ΔT_ad = −ΔH°_rxn/Σ(n·c_p)

ν is the stoichiometric coefficient of each product (P) or reactant (R), and ΔH°_f its standard enthalpy of formation at 298.15 K, in kJ/mol [1], [2]. ΔH°_rxn is in kJ per unit of reaction as written: if the equation has 2 mol of a reactant, the heat is for 2 mol of it. A negative value is exothermic. Σ(n·c_p) is the heat capacity of everything leaving the reactor per unit of reaction, in kJ/K, including inerts and excess reactants. ΔT_ad is the temperature rise if all the heat stays in that stream [2].

Inputs

• Choosing a species fills in its ΔH°_f from Table C.4 of [1]. Elements in their standard state, such as O₂ and H₂, are zero.
• For a reaction with only one reactant or product, set the unused coefficient to 0.
• Enter 0 for Σ n·c_p to skip the temperature change.

Limits and common mistakes

• Watch the phase of water. Liquid water gives the higher heating value of a fuel; vapor gives the lower one. They differ by 44 kJ per mole of water.
• The heat is at 25 °C. At other temperatures it shifts by the difference in heat capacity between products and reactants [1].
• ΔT_ad uses one mean c_p. Over a large rise, use a c_p averaged over that range. The result assumes the reaction goes to completion with no heat loss, so it is an upper bound.
• Check that the equation is balanced. The page does not check atoms.

Worked example

A high-temperature shift converter turns carbon monoxide and steam into carbon dioxide and hydrogen. The gas leaving it is about 15 mol for each mole of CO converted, with a mean c_p of about 0.035 kJ/(mol·K), so Σ n·c_p is 0.525 kJ/K. How hot does the bed get?

1. Enter coefficient 1 for each slot.
2. Choose Reactant 1 — species Carbon monoxide (CO), gas, and Reactant 2 — species Water (H₂O), gas.
3. Choose Product 1 — species Carbon dioxide (CO₂), gas, and Product 2 — species Hydrogen (H₂), gas.
4. Enter Σ n·cp of Product Stream 0.525 kJ/K and press Solve. The Solution shows: Σ (ν·ΔH°f) products: -393.509 kJ
   Σ (ν·ΔH°f) reactants: -352.343 kJ
   Standard heat of reaction ΔH°rxn: -41.166 kJ per unit reaction
   Nature: Exothermic
   Adiabatic temperature change ΔT_ad: 78.4114 K

Check by hand: −393.509 − (−110.525 − 241.818) = −41.166 kJ, the textbook heat of the water-gas shift. Then 41.166/0.525 = 78.4 K, in line with the 50–100 K rise usual across a shift bed.