Calculate the standard free energy change for the dissociation of HEPES.

Gibbs free energy, sometimes referred to as the Gibbs function, Gibbs energy, Standard free energy, or free enthalpy, is a unit used to quantify the most work that can be performed in a thermodynamic system while maintaining constant temperature and pressure.

HEPES stands for (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid ) and is a zwitterionic organic chemical buffering agent with a reaction quotient of ${\text{3.39×10}}^{\text{-8}}$ .

Use the following formula to calculate standard free energy:

${\text{ΔG}}^{\text{°}}{\text{prime=-RT}}^{\text{T}}{\text{ln}}_{\text{e}}\text{q}$ , where R represents the gas constant and q represents the reaction quoteint.

We get,

$\begin{array}{c}{\text{ΔG}}^{\text{°}}{\text{prime=-RT}}^{\text{T}}{\text{ln}}_{\text{e}}\text{q}\\ \text{=(-8.3145\hspace{0.17em}J\hspace{0.17em}mol\hspace{0.17em}K)(298K)ln}\left({\text{3.39×10}}^{\text{-8}}\right)\\ {\text{=42,616.43\hspace{0.17em}J}}^{\text{*}}{\text{\hspace{0.17em}mol}}^{\text{-1}}\end{array}$

Therefore, the required standard free energy change for the dissociation of HEPES is ${\text{42,616.43\hspace{0.17em}J}}^{\text{*}}{\text{mol}}^{\text{-1}}$, i.e., ${\text{42.616KJ}}^{\text{*}}{\text{mol}}^{\text{-1}}$