Why should temperature be specified when doing weak acid pH calculations?

K_w varies with temperature, and the variation isn't small. According to Whitfield,

log K_w = -4470.99/T + 6.0875 - 0.01706 T

Temperature affects both the ionization of water and the ionization of the acid, so K_a will vary with temperature too. Depending on

H for the reaction, the K_a variation may be a more important temperature influence on weak acid equilibrium calculations than the K_w variation. Every numerical value of an equilibrium constant should be accompanied by a temperature.

Most acid-base titrations are done at room temperature for convenience (glassware is usually calibrated for 20°C), and when people say "Kw is 1.01×10^-14" or "pH + pOH = 14", they're talking about room temperature. These numbers are easy to remember and they're appropriate for most situations you'll encounter in general chemistry. It's an i you'll often find undotted.

But consider calculating the pH of blood plasma inside a living organism. You'd have to take the temperature variation of Kw into account (pKw is 13.60 at body temperature (37°C), and 13.996 at room temperature (25°C)). It's a little more difficult to take into account the temperature variation of the various Ka's in the plasma buffering system. The analysts just measure the pH at 37°C rather than taking the measurement at a different temperature and bothering with a temperature correction.

References

M. Whitfield, in Chemical Oceanography, J. P. Riley and Skirrow, Eds., Vol. 1, 2nd ed., Academic, New York, 1975, pp. 44-171.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! Why should temperature be specified when doing weak acid pH calculations?