The pKa of a Weak Acid as a Function Jeffrey 1. Bada
of Temperature and Ionic Strength
University of California, San Diego La Jolla, California 92037
I
An experiment using a pH meter
W h e n a weak acid HA is dissolved in water, it dissociates according to the following reaction Precise values of the equilibrium constant for this dissociation are determined from measurements of the electromotive force of a suitable galvanic cell. The techniques nsed by the National Bureau of Standards have been described by Bates.' However, fairly good results can be obtained using a laboratory pH meter with an expanded scale, and this technique has been nsed recently to determine the pK's of fumaric acid between 0 ' and 95°C.2 This technique has also been nsed successfully as an experiment in the undergraduate physical chemistry laboratory a t this University. The experiment illustrates a number of physical chemistry principles as well as giving students the opportunity to use the computer. This paper reports the procedure used in this experiment. The equilibrium constant for eqn. (1)is given by
BATES, R. G., "Determination of pH," John Wiley & Sons, Ine., New York, 1964. 8. L.,Rioehemistl7~,7, 3403 (1968). BADA,J. L., .4ND MILLER, "EWIS, G. N., AND RANDALL, M., then no dynamic^" (revised by PITZER, K. S., and BREWER,L.), MoGraw-Hill, New York, 1961, Chapter 23. 'KLOTZ, I. M., 'Chemical Thermodynsmics," W. A. Benjamin, Inc., New York, 1964, p. 25.
where the a's are the respective activities of H+, A-, and HA, and the $s, the respective activity coefficients; the brackets refer to molar concentrations. Equation (2) can be rewritten as pK,' = pH
When [A-]
=
[A-1 - log = pK. - log [HA1 YEA
F A ] , pK,
=
pK," = pH
-/A - log (3) YHA
PH, and
- log r ~ - / u n ~
The activity coefficients in the above equations can be approximated from the Dehye-Hiickel expressionS
where Z; is the charge on ion i and I, the ionic strength. I is defined by the relationshipa
where mi is the concentration of ion i. I n dilute solution, the activity coefficient of an uncharged species may be approximated as unity a t all temperatures. The temperature dependence of pK. can be expressed in the form pK. = A + BIT + CT (6) Experimental pK,'s can be fitted by the method of least squares4 to obtain an equation in the form of eqn. (6). The AH and AC, for the dissociation of the weak acid a t
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any temperature can be calculated by differentiation of this equation. Determinations of the pH of a solution using a pH meter are not measurements of the absolute pH, but rather the difference between the DH of the unknown solution and the pH of some stand&-d solution which is used to standardize the meter. Accurate pH measurements by a pH meter therefore require the use of accurate p H standards. Several primary pH standards have been recommended by the National Bureau of Standards' which cover the pH range 3-10. If the pH of the unknown solution is between 3 and 6, potassium acid phthalate is a suitable standard. Outside this range, one of the other primary standards should be used. The Experiment Any laboratory pH meter, which has a scde expander, can he osed to make the following pH measurements. The electrodes, however, should be capable of withstanding temperatures up to 70%. For the measurements s t room temperature and above, a bath regulated to &O.lO°C or better should be used. A Dewar flask containing water cooled to the desired temperature is osed for the t,emperatures below room temperature. Prepare 500 ml of a standard 0.05 M solution of potassium hydrogen phthslate. The potassium hydrogen phthalate should he dried at 100% for about 2 hr before use. The phthalate solution should be carefully prepared, using COS free water if possible, because it will be used to standardize the pH meter at the various temperatures. The pH of this solution between 0' and 9 5 T is given by pH = -9.836
+ 1678.3/T + 0.03495 T - 2.480 X 10-%TZ
A graph of the pH of this solution versus temperature should he made before starting the experiment. Prepare a solution in which the concentrations of the weak acid, HA, and its salt, A; are both 0.02 M. This solution should also he prepared carefully and the actual concentrations of HA and Aknown accurcltely. Add NaCl to the solution to adjust the final ionic strength of 0.10. Use 200-ml Berzelius beakers as containers for the weak acid and potassium hydrogen phthalate sohtions in the temperature bath. The solutions in these beakers should be changed several times during the course of the pH measurements. Measure the pH of the weak acid buffer solution between 0" and 70°C at approximately 10' intervals. The pH meter should be strtndrtrdieed with the potassium aeid phthalate solution before and after the pH measurement at each temper* ture. If the standardization after the pH measurement requires an adjustment ofmore than 0.010 pH units, the measurement should he repeated. Before measuring the pH, the electrodes and solutions should be allowed to equilibrate thermally with the bath for 15 min. Prepare four solutions having the same concentrations of HA and A- as the one above. By adding NaCI, make up a. serie? of nolotions whose final ionic rtreneths rmae from 0.03 to 0.4. (Note that a solution with1 = 0.lneed notbe prepared since the
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solution used in the temperature studier can he used for this ionic strength.) Measure the pH of these solutions a t room temper* ture.
Calculations Calculate the p K . of the weak aeid from eqn. (3) and the measured values of the pH at each temperature, Plot these p K , values versus l/T("K). By the method of least squares, calculate the temperature dependence af p K . in the form of eqn. (6). From this equation, calculate AH and AC, s t 25' and 50°C. Calculate p K . as a function of ionic strength at roam temperature, and plot versus ionic strength. Extrapolate this plot to I = 0.0 and determine pKa0, the p K . at infinite dilution. Using this value, eqn. (3), and 7 ; calculated from eqn. (4),calculate the theoretical dependence of p K . with ionic strength and plot versus ionic strength. Compare the experimental and theoretical ionic strength dependence of p K , and discuss any differences that are observed.
Comments
This technique can be used to give good estimates of the temperature variation of the pK, of most weak acids. However, due to the liquid junction potential problems involved in the use of the p H meter, the results should not be considered nearly asaccurate as those determined from electromotive force measurements of cells without liquid junctions. The weak acid used in the experiment should be one which has a fairly large change in pK, with temperature. I n the experiment a t this University, the students obtained good results using sulfanilic acid. Most of the pK, values determined by the students between 0 ' and 70°C were within a few hundredths of the pK unit of the literature value^.^ Two of the major sources of difficulty were not allowing the electrodes and solutions to equilibrate thermally with the temperature bath, and careless standardization of the pH meter. If the pH of the weak acid solution is greater than 8, care should be taken to minimize COz absorption; in this case, the weak acid solutions should be changed after every p H measurement and the solution covered as much as possible while it is in the temperature bath. The students a t this University were provided with a computer program which did the least squares calculations. The experiment therefore allowed students to use the computer and introduced them to one of its applications in physical chemistry. 6
MACLAREN, R. C.,
Soc., 73, 1822 (1951).
AND
SWINEHART, D. F.,J. Amer. Chem.
