# How does pH affect the change in free energy for a reaction?

Jun 12, 2014

The change in Gibbs Free Energy for a reaction (DeltaG_(rxn)) depends on the concentration of reactants and products, so an increase in pH increases $\Delta {G}_{r x n}$ if ${H}_{3} {O}^{+}$ is a reactant, and decreases $\Delta {G}_{r x n}$ if ${H}_{3} {O}^{+}$ is a product.

The general relationship between Gibbs Free Energy change for a reaction and the concentrations of reactants and products is

$\Delta {G}_{r x n} = \Delta {G}^{0} + R T \ln Q$

where $\Delta {G}^{0}$ is the free energy change for the reaction under standard conditions (unit concentrations of reactants and products), and $Q$ is the reaction quotient (actual product concentrations divided by actual reactant concentrations).

Example: ${H}_{3} {O}^{+} \left(a q\right) + N {H}_{3} \left(a q\right) \leftrightarrow {H}_{2} O + N {H}_{4}^{+} \left(a q\right)$

$Q = \frac{\left[N {H}_{4}^{+}\right]}{\left[{H}_{3} {O}^{+}\right] \left[N {H}_{3}\right]}$
Note that ${H}_{2} O$ does not contribute to $Q$ because it is a solvent.

An increase in pH decreases the hydrogen ion concentration, $\left[{H}_{3} {O}^{+}\right]$, thereby increasing $Q$ (because it appears in the denominator of $Q$), and increasing $\Delta {G}_{r x n}$.

An increase in $\Delta {G}_{r x n}$ decreases the thermodynamic driving force for the reaction, and if $\Delta {G}_{r x n}$ becomes positive the reaction is no longer spontaneous (i.e., the reverse reaction becomes spontaneous).