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QUESTION

# How does pH affect Gibbs free energy?

is directly proportional to the .

(PH) or (-log[H^+])=(-E/0.059)

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pH affects the Gibbs free energy. The pH is given by the Henderson-Hasselbalch equation:

pH = pKa + log { [A-]/[HA] }

where Ka is the equilibrium constant for the reaction

HA ---> H+ + A-

As we know ka = [H+][A-] / [HA]

and pKa = - log Ka .

Ka is itself a function of temperature, since it is related to the Gibbs free energy of reaction (delta G) by the equation

delta G = - RT ln Ka = -2.303 RT log Ka = 2.303 RT * pKa

so we have

pkA = delta G / (2.303 RT)

delta G is itself given by

delta G = delta H - T * delta S

where delta H is the enthalpy of reaction and delta S is the entropy of reaction. Combining these, we get

pKa = (delta H / (2.303 RT)) - (delta S / (2.303 R))

The variation with temperature is determined by the sign of delta H. For example, if delta H is positive (endothermic dissociation), pKa gets smaller as the temperature gets larger.

Decrease in pKa amounts to an increase in Ka, which means that the reaction favors dissociation more as temperature increases (in agreement with LeChatelier's principle). This increases [H+] and decreases the pH.

If the reaction is exothermic the opposite effect will be observed. Either way, we expect the pH to depend on temperature.

Biological systems can use enzyme-catalyzed reactions to keep the pH constant even when T varies.