Temperature dependence of heat of reaction: Which named relation provides the effect of temperature on the heat (enthalpy) of reaction?

Introduction / Context:Engineering calculations often require adjusting heats of reaction from a reference temperature to a process temperature. The appropriate tool is Kirchhoff’s equation, which connects the temperature dependence of reaction enthalpy to the difference in heat capacities of products and reactants.

Given Data / Assumptions:

• Standard reference temperature T_ref with known ΔH_rxn(T_ref).
• Heat capacities (Cp) of species as functions of temperature.
• Ideal-mixture assumption for enthalpy calculations.

Concept / Approach:Kirchhoff’s equation: ΔH_rxn(T) = ΔH_rxn(T_ref) + ∫_{T_ref}^{T} ΔCp dT, where ΔCp = Σ ν_p Cp_p − Σ ν_r Cp_r. This relation states that the change in reaction enthalpy with temperature equals the integral of the net heat-capacity change over that temperature range. Other named equations serve different purposes: Maxwell’s relations are thermodynamic identities; the Antoine equation correlates vapor pressure with temperature; Kistiakowsky refers to certain empirical kinetics/thermochemistry correlations, not the general ΔH(T) dependence.

Step-by-Step Solution:

Verification / Alternative check:For small temperature intervals and nearly constant ΔCp, use ΔH_rxn(T) ≈ ΔH_rxn(T_ref) + ΔCp * (T − T_ref) as a reliable approximation.

Why Other Options Are Wrong:

• Maxwell’s relations connect derivatives of thermodynamic potentials; they do not give ΔH(T).
• Antoine equation correlates vapor pressure; unrelated to reaction enthalpy.
• Kistiakowsky correlations are not the canonical ΔH(T) relation for general reactions.

Common Pitfalls:Confusing standard heats (at 298 K) with process conditions; neglecting temperature-dependent Cp, especially for wide temperature ranges.

Final Answer:Kirchhoff’s equation.