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.