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Name: Mark C.
Status: N/A
Age: 16
Location: N/A
Country: N/A
Date: Monday, December 30, 2002

What is the relationship between temperature and pH?
Should a pH change with temperature change?
If so, and the temperature does not change, why?

The ionization of an acid can be written schematically as: HA -----> H(+) + A(-) for a monoprotic acid. The equilibrium constant for that reaction written in terms of the concentrations is: Keq = [H(+)] [A(-)] / [HA]. The pH is: pH = -log[H(+)]. The general equation for the change of an equilibrium constant is: d(ln(Keq))/dT = (DH)/RT^2 where: the "d's" mean the change in the natural log of Keq, and the temperature T in kelvins, DH in the heat of reaction, and R is the gas constant. Since pH is already a "log" function of Keq, and the change in Keq is again a "log" function of the heat of reaction, DH the change in pH is not a very sensitive function of temperature. In addition, the heat of the ionization reaction DH for partially dissociated acids like acetic acid, formic acid etc. is very small. In fact, to a reasonable approximation for partially dissociated acids DH is less than 1-2 kcal per mol, which is very small. So pH does not change very much with temperature (This is not the same effect as the temperature correction of an electrode on a pH meter, which arises from the properties of the electrode not the ionization of the acid.). You can find details in an article in the Journal of Chemical Education, Vol. 48,pg.338, 1971.

Vince Calder


pH can indeed vary with temperature. The reasons why depend on the context, but even a simple solution of a weak acid (HA) will exhibit a (weak) temperature dependence. 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-

( 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))

If we assume for the sake of simplicity that delta H and delta S are approximately independent of temperature T (constant), then 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. A 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.

These arguments can be extended to strong acids too. Things get complicated when there are multiple chemical reactions. Biological systems can use enzyme-catalyzed reactions to keep the pH constant even when T varies (within limits, of course).

best, Prof. Topper

In most cases, the pH of a solution will change as temperature changes. However, there is not a general relationship between temperature and pH: it depends on the composition of the solution.

pH is the negative common (base 10) logarithm of the hydrogen ion (H+) activity in a solution. The hydrogen ion activity depends on all the possible chemical reactions that produce or consume hydrogen ions. The extent of a chemical reaction depends on its equilibrium constant, and the equilibrium constant of any reaction depends on the temperature. Some reactions become more likely as temperature increases, some less.

The most basic chemical reaction affecting pH is the dissociation of water:
H2O --> H+ + OH-
Over the temperature range 0 to 60 degrees Celsius, this reaction becomes more favorable. This means that neutral water will contain a higher concentration of H+ as the temperature increases, so the pH will decrease.

The reactions by which acids dissociate to create H+ and bases consume H+ depend on temperature in a variety of ways. Some increase with temperature, some decrease, and some increase or decrease away from a maximum or minimum value at a specific temperature. To predict the pH change of a specific solution with temperature, you would need to know all the components of the solution, all the reactions involving those components that produce or consume H+, and how the extent of these reactions varies with temperature.

Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois

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