tions containing 3 grams of KAl(S04)2.12 HzO and 2.00 mmol of " 0 3 was determined by performing 6 sample and 4 blank titrations. Potassium fluoride was used as complexing agent. The value thus determined was 2.010 f 0.020 mmol " 0 3 . This gives an accuracy of 0.5% assuming the salt to be completely neutral ( 7 ) . Blaedel and Panos ( I ) found a free acid content of 2 mequiv/mol PO(7) T. Eder. Fresenius'Z Anal. Chem., 119, 399 (1940).
tassium alum which is 0.013 mmol H'/3 grams. Any attempt, however, to compare these results is futile since, first of all, different batches of alum are involved and, second, the accuracy of enthalpimetric titrations is certainly not better than 0.5%. Received for review July 23, 1973. Accepted November 12, 1973.
Determination of Cation Activities in Solutions by the Ion Exchange Resin Method K. N. Pearcel Department of Chemistry and Biochemistry, Massey University, Palmerston North, New Zealand
L.
K. Creamer
New Zealand Dairy Research Institute, Private Bag, Palmerston North, New Zealand
The following symbols will be used: ~ , % 1= electrochemical potential of cation A in phase I uAI = activity of cation A in phase I 2.4 = valency of cation A $1 = electrical potential of phase I F = Faradayconstant T = Thermodynamic temperature Under conditions of equilibrium, p\l
pBI
= =
p,A1l
=
p,All'
pgll= pelll
.
etc. Expanding
Rearranging
Z,kF( $J"' - d ' ) If the standard states in phases I and I11 are similarly defined, this equation can be simplified to Phase I Solution
Phase I11 Phase I1 Cation exchange resin Solution
Similarly for component B
Dividing Equation 1 by Equation 2
or
(3) A N A L Y T I C A L CHEMISTRY, VOL. 46, NO. 3, M A R C H 1974
457
Table I. Calibration Parameters and Standard Deviations for the Amberlite IR 120 Resin-Na+-KfMg*+-Cas+ System at Room Temperature an1 UKzM
M
Ca
p)B
1870 X 366 X
Additions per liter
B
2.14 f 0.24 f 99 X 10-6 f 13 x 10-6
pH
Nil 6.67 N a 2 C 2 0 4 , 2 m M 6.72 CaC12,2mM 6.61 CaC12,5 m M 6.53 6.47 HCl, 4 mM 6.91 NaOH, 4 m M
XKZM
a
Na M g
-
Table 11. Effects of Adding Electrolytes on the Cation Activities of Bovine Skim Milk
0.969 f 0.071 1.290 f 0.037 1.344 f 0.026
UN./YK
19.6mM 28.5mM 23.1mM 22 .O m M 21.4mM 27.9 m M
~ M S / ~ K ~
0.70mM 0.67mM 0.77mM 0.88 m M 0.81mM 0.64 m M
~c./YK'
1.77mM 1.66mM 2.34mM 3.39 m M 2.52mM 1.65 m M
lectivity of the resin depends on its composition (7'). Any functional relationship (such as between resin and solution composition) can be approximated over a specified interval by a polynominal of the independent variables having sufficient degree. Taylor's theorem provides a convenient method of finding the coefficients. This is the basis of the method used by Van Kreveld and Van Minnen (2) who used a first degree polynominal. A more convenient and concise method of relating the composition of the resin to that of the equilibrium solution is provided by equations of the form a*ZH
XAZH
aR% 1 = a(-) XBZi
Solution under investigation
Cation exchange and resin
Standard solution
Cation exchange resin
u'
(4)
where X.4 is the mole fraction of cation A on the resin, (Y and /3 are empirical constants, found by least squares analysis. The non-ideality of an ion exchanger is indicated by the departure of /3 from unity (8). Table I contains the values and standard deviations of the six constants found for the Amberlite IR 120 resinNa+-KT-Mg2--Ca2+ system at room temperature from 21 data points. The activities are expressed on a millimolar scale. The activity of a single ionic species cannot be determined from thermodynamic study alone but requires the adoption of some extra-thermodynamic assumption or convention. Although the significance and meaning of single ion activities is controversial, consistent scales of single ion activities, such as the pH scale; can be constructed and have been found useful. The use of thermodynamically definable quantities such as
yBZi
where y H is the activity coefficient of cation B, avoids the difficulties with single ion activities. The results obtained from bovine skim milk to which various additions have been made are given in this form in Table 11. Single ion activities can be readily calculated by assuming an appropriate value for y K, the potassium ion activity coefficient in the milk ( y =~ 0.79). Although there have been promising developments in the field of ion specific electrodes in recent years, it seems likely that the ion exchange resin method for determining cation activities will continue to be the method of choice for the study of complex solutions containing many ions. ACKNOWLEDGMENT The authors gratefully acknowledge the helpful advice of G. N. Malcolm. Received for review August 13, 1973. Accepted October 4, 1973. This note is based on a thesis submitted in 1972 by K. N. Pearce to Massey University in partial fulfillment of the requirements for the Ph.D. degree. (7) D. R e i c h e n b e r g , "Ion-exchange Selectivity." in "Ion Exchange," J. A. Marinsky, Ed., Arnold, London, 1966, Vol. 1 , C h a p t e r 7 . (6) G. K a r r e m a n a n d G. E i s e n m a n , Bull. Mafh. Biophys., 24, 413 (1962).
458
ANALYTICAL CHEMISTRY, VOL. 46, NO. 3, MARCH 1974
