Question

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

Answer 1

Hint: In an aqueous solution, the acidity or the basicity can be specified using a pH scale. The pH scale denotes the potential or the power of hydrogen. Acidic solutions have a lower pH while basic solutions or alkaline solutions have a higher pH value.

Complete answer:
First, we need to understand what free energy is. Free energy is a thermodynamic function of the state. The maximum amount of work performed by a thermodynamic system at constant temperature is given by the change in the free energy.
The change in free energy, at constant pressure and constant temperature, can be calculated using Gibbs free energy. It's given by
\[\Delta G=\Delta H+T\Delta S\]
Where \[\Delta G\] is the change in the Gibbs free energy, \[\Delta H\] is the change in enthalpy, T is the temperature of the system in Kelvin, and \[\Delta S\] is the change in the entropy.
Now, the relationship between the concentration of reactants and products and the Gibbs free energy can be given by
\[\Delta {{G}_{rxn}}=\Delta G{}^\circ +RT\ln Q\]
Where \[\Delta {{G}_{rxn}}\] is the change in Gibbs free energy for a reaction, \[\Delta G{}^\circ \] is the change in Gibbs free energy under standard conditions, R is the ideal gas constant and Q is the reaction quotient.
We know that the reaction quotient Q of any reaction is the ratio of the concentration of product to the concentration of the reaction. So, for a reaction in an aqueous state,
\[aA+bB\rightleftarrows cC+dD\]
\[Q=\dfrac{{{[C]}^{c}}{{[D]}^{d}}}{{{[A]}^{a}}{{[B]}^{b}}}\]
Let us take an example. For the reaction
\[{{H}_{3}}{{O}^{+}}+N{{H}_{3}}\rightleftarrows {{H}_{2}}O+NH_{4}^{+}\]
\[Q=\dfrac{[NH_{4}^{+}]}{[{{H}_{3}}{{O}^{+}}][N{{H}_{3}}]}\]
Water, being a solvent, does not contribute to the reaction quotient.
Since \[pH=-\log [{{H}_{3}}{{O}^{+}}]\], increasing the pH will decrease the hydrogen ion concentration, and hence will increase the value of Q.
We know that reaction quotient is directly proportional to the $\Delta {{G}_{rxn}}$, and hence increase in the value of Q, for this reaction, will increase the value of $\Delta {{G}_{rxn}}$ as well.

Note:
It must be noted that the relation between the change in pH and its effect on reaction quotient Q is completely dependent on the products and the reactants involved in the reaction.
pH value increases with the increase in $[O{{H}^{-}}]$ and decreases with the increase in $[{{H}_{3}}{{O}^{+}}]$ ions.