Role of Mixing Entropy in the Equilibrium of Gas-Releasing Reactions in Solution

Standard computational approaches treat all chemical reactions as single-phase systems with ideal mixing of all species; however, most reactions in the laboratory occur in solution with a liquid and a gas phase in equilibrium. Therefore, such approaches systematically neglect entropic and energetic contributions that arise if gaseous products partition between the liquid and vapor phases. This work addresses this fundamental limitation by developing two thermodynamically rigorous models to quantify these contributions in solution-phase reactions releasing gaseous byproducts: a closed system model representing typical laboratory conditions with finite vessel volumes and an open system model corresponding to reactions exposed to the atmosphere. The standard single-phase treatment is also examined as a theoretical reference. The formalism was validated by modeling the synthesis of bicyclic Ir(III) hemiaminal complexes and Fischer-type carbenes from TpMe₂Ir(diene) reactions with aromatic aldehydes, where CO₂ release determines product selectivity. Uncorrected density functional theory (DFT) calculations systematically predicted incorrect product distributions, favoring non-CO₂-releasing pathways. Application of the closed system model provided non-negligible entropic corrections that improved the agreement with experimental observations, correctly predicting predominant hemiaminal formation for most substrates and mixed distributions for 4-dimethylaminobenzaldehyde. Analysis reveals that the favorability of gas-releasing pathways is partially driven by the mixing entropy gain as dissolved gas molecules expand into the headspace, with equilibrium positions exhibiting a strong volume dependence. This transferable methodology requires only Henry's constants and experimental conditions, making it broadly applicable to any reaction system where a gas is released as a byproduct or consumed as a reactant.