Deducing the pK-Temperature
It has been well-documented (1,2)that the variation with temperature of acid dissociation constants can be precisely described by equations of the form
+
(1) pK = AIT + B C log(T) where the parameters, A, B, and C have different hut constant values for each particular case. Although many authors have preferred equations with additional terms, such as D T and DT2, or even equations with quite different algebraic forms, there is little need to use anything other than eqn. (1) for experimental data in the 0 4 0 ° C range. Incidentally, eqn. (1) is quite equivalent to its expanded cousin, the &term Clarke and Glew equation (2). Textbwks commonly recommend that the numerical values of A and B he determined as the slope and intercept, respectively, of a plot of p K versus 1/T. For chemical reactions in the gas phase, where the C log(T) term is negligible, this is useful advice. But for reactions in solution this term is usually required to account for the observed temperature effects. However, the values of A and B may he determined from a linear plot if the quantity [pK - C log(T)] is plotted versus 1/T. Obviously a numerical value of C is required before such a "sigma plot" can be made. Thanks to a recent paper by Ives and Moseley (3),who take a fresh lwk a t a principle suggested by Everett and Wynne-Jones (I),the calculation of C from the raw pK(T) data is quite simple. The key step is to transform eqn. (1) into either of the following derivative forms
+
d(TpK)ldT = B + CIL C log(T) dpKldT = -AIT2 + CILT where L = ln(10).
(2) (3)
The Ives-Moseley Method Finding C: First Difference Calculations
Ives and Moseley prefer to work with eqn. (2), which can be related to the entropy change, ASo (at constant pressure) ASo = -dAGVdT = -RL d(TpK)ldT = -RLB - RC - RCln(T) (4) where R is the gas constant. If the data set contains N values of p K and T, then (N 1) values of A S 0 may be approximated by the simple use of difference calculations
ference calculation. Incidentally, i t is not required that the tem~eraturesbe eauallv s ~ a c e dFrom . eun. (6)we see that a plo 4. I f - 1S7il 8 . r * ~ r a a n n . T h.7 ?..ea,rcmen 62.111 11958 15 C.c\e'r H I. J CHEhl EDI'C.4i.231 1988 . J. Chem. Soc.,Foradoy Trans.. (10) Berboruah, C. P., Camoes. M.,abd c o v i n p t o n , ~K., 69,I. 949 (1973). (11) 0atea.R. G..andPinehin& G.D . , J Amw. Chem. Soe.. 72.1393 (1860). ~
~~
Volume 54, Number 5, May 1977 1 283
