The ion Product Constant of Water
H. Lawrence Clever
Emory University Atlonto, Georgia 30322
Thermodynamics o f water ionization
W a t e r undergoes self-ionization which may be simply described by the dissociation reaction H%O* H C + OH-
or by the proton exchange reaction H,O
+ H20
F3
H$0+
+ OH-
or by the reaction (m
+ n + 2) H1O e H 3 0 + . m H q 0+ O H - . n H 2 0
where m and n are hydronium and hydroxide ion hydration numbers ( I ) , respectively. The extent of the reaction is small, and the ionization constant, commonly called the ion product constant, is K , = a ~ + a ~ ~ where - / a the ~ , activity ~ of water, a ~ , o is , unity in pure water. The standard thermodynamic relations for an equilibrium constant apply.
+
AC,'
=
CPoa+
AHo
=
AH,"
+
J
OH- - C g D ~ a AC,' dT
emf of cells without transference, and thermal measurements. Condudomefric Techniques
Reliable values of the ion product constant of water were obtained in the early classical conductivity work of Kohlrausch and Heydweiller (3). The specific conductance, K, has units of ohm-' cm-1, and represents the conductance across opposite faces of a 1-cm cube of the sample. In practice one measures the specific resistance, p, which is the inverse of specific conductance, p(ohm-cm) = 1 / ~with , a Wheatstone Bridge modified for use with an alternating current. The specific conductance is converted to an equivalent conductance, A, by A = KVm, where V,,, is the water molar volume. The degree of dissociation, LY, is gotten from LY = A/AO where A. is the limiting equivalent conductance of water obtained from the relation where the Ao's are the limiting equivalent conductances of the indicated strong electrolytes. The ion product constant of water is K.
and
From a knowledge of K, and its temperature coefficient one can calculate the thermodynamic changes AGO, AH0, ASo, and AC,' of the standard ionization reaction. Conversely, from a knowledge of ACPo and its temperature coefficient and one value of AHo and one value of either K,, AGO, or ASo, K, and its temperature coefficient can he calculated. In fact, both approaches have been used and will be reviewed here. Figure 1 illustrates our present knowledge of the ion product constant of pure water as a function of temperature. For the liquid, K , increases from 10-l5 at O°C, 10-l4 at 25'C, and 10-I2 at 120°C to a maximum of about 6.5 X 10-l2 at 220°C and then decreases to a value near 3.5 X 10-I4 at 374"C, the critical temperature of water. In the supercritical region K , increases with temperature along the lines of constant density shown in the upper right of Figure 1.
=
C Z + COX- = ( C o a ) ( C D a = ) Co%a'
where Cois the number of moles of water in 1000 g. Kohlrausch and Heydweiller applied the conductivity technique to water samples carefully purified by some 47 successive distillations. Their ion product constant values between 0' and 50°C are only several percent higher than presently accepted values. Duecker and Haller (4) recently reported electrical conductivity measurements on electrophoretically purified water with known varying impurity content. The temper* ture coefficient of conduction was determined from
Determination o f the Water Ion Product Constant
Many techniques have been used to obtain values of the ion product constant of water. Early methods and results are summarized by Beans and Oakes (S). Here we will discuss only three methods: conductivity,
Figure 1. Log of the ion product constant venur temperature. The solid line represents liquid wqtor in equilibrium with it* own vapor pros. sure. The broken lines represent supercritical woter nt densities ef 0.30.79 The dotted liner represent isobars at Rve pressures between 5 0 0 ond 2 0 0 0 dm.
Volume 45, Number 4, April 1968
/
231
measurements at 18' and 25'C for each fraction, and the theoretical conductivity of pure water was calohm-'cm-' at 25'C. The culated as 0.0547 X value is consistent with the presently accepted ion product constant of water obtained by emf measure ments on galvanic cells without transference. Noyes, ICato, and Sosman (5) determined the electrical conductivity of many weak and strong electrolytes in aqueous solution at many temperatures up to 306°C. They obtained values of K, at several temperatures above 100°C from their study of the ammonium acetate hydrolysis. NH4+
+ C1H102- + HzO
NHIOH
+ HC~H~OI
Recently Franck (6) has studied the conductance of ICCI, ICOH, and HCI in supercritical water between 200" and 700°C. These electrolytes behave as weak electrolytes (Fig. 2) at water supercritical temperatures and pressures and approach "strong" behavior at pressures corresponding to supercritical water densities near 1g cm@.
David and Hamann (7) have measured the specific conductance of water at a high shock pressure of 127,000 atm and 7 7 2 T where supercritical water density is 1.717 g ~ m - ~ They . suggest that under these conditions the water specific conductance of 0.53 ohm-' cm-I corresponds to an ion product constant of about lo-%. Franck's equation predicts a value of Considering the experimental difficulties and the dangers of extrapolating Franck's equation, the agree ment is considered satisfactory. The values of the water ion product constant for the supercritical region in Figure 1 were calculated from Franck's equation. The isobars were estimated from Kennedy and Holser's (8) recommeuded PVT data for supercritical water. EMF Studies of Cells withouf Transference
Several cells without transference of the hydrogen electrode type-slightly soluble metal salt-metal electrode-have been used to obtain values of the ion product constant of water. Probably the most reliable and most quoted values for the water ion product constant in the 0'-60°C range come from the work of H. S. Harned and students (9) of Yale University. They used cells of the type
where h I = Lif, Na+, or I
