THE TEACHING OF THE THEORY OF THE DISSOCIATION OF ELECTROLYTES. I. THE APPLICATION OF THE LAW OF MASS ACTION TO SOLUTIONS OF ELECTROLYTES MARTIN KILPATRICE, JR., UNIVERSITY OX PENNSYLVANIA, PHILADELPHIA, ~NNSYLVANIA
I n presenting the theory of the dissociation of electrolytes the teacher should attempt to develop the subject in such a m y that the advanced student does not have to unlearn a considerable number of the "facts" presented in the more elementary courses. The law of mass action i s discussed in ils application to solutions of electrolytes and i t i s shown that one must consider the assumptions involved in the derivation of the law. Illustrations of the applimtion of the law to solutions of weak electrolytes are giyen and the importance of the change of the dissociation constant with change in electrolyte concentration i s pointed out. The older and newer ideas on strong electrolytes are discussed and the importance of the change in the mo6ility of a n ion with change i n ionic concentration i s emphasized. The solubility product i s also discussed.
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In teaching modem theoretical chemistry the author has often found that a great part of his efforts are spent in correcting the student's erroneous ideas concerning the dissociation of electrolytes in aqueous solution. Indeed the teaching of this subject, instead of being a gradual development of ideas, hypotheses, and laws from the first course to the last, seems to have become the presentation of a series of empirical and often contradictory statements. Perhaps the law of mass action is thc most mistrcatcd and most misrepresented law of all. This paper is gritten in an effort to present the subject in such a way that the student of general and analytical chemistry may have a foundation upon which to build up the more detailed treatment of the subject. The usual derivation of the law of mass action for the system A+B*C+D
leading to the evaluation of the equilibrium constant Kc as cccD/c~cB is made from kinetic or from thermodynamic considerations. In either case there is an assumption in the derivation, no matter how the concentrations are expressed. In the kinetic derivation the assumption is that the rate of reaction is proportional to the product of the concentrations of the reactants, and in the thermodynamic derivation the assumption is that the free energy changes can be truly expressed in terms of the concentrations. Consequently Kc, the equilibrium constant above, is a true constant only in so far as these assumptions are valid, ?hat is to say, for perfect solutions. The teacher, therefore, should emphasize the f a d that K,is constant only within the limits of the validity of the assumptions involved. Let us consider the case of a weak electrolyte in aqueous solution, for example, acetic acid. The classical dissociation constant 840
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Kc = CE+CCH~COO-/CCH~OOOH*
and in a table of dissociation constants we h d that Kc is given as 1.8 X lo-'. Solving for the concentration of the hydrogen ion we get C E + ~=
KICC~COOH
whence for a solution 0.05 M in acetic acid CHI
= 9.2 x 10-
and for a solution 0.1 M in acetic acid ca+ = 1.3 X lo-'.
So far everything is correct if we have the correct value of Kc. But let us proceed, considering K, constant, to calculate the hydrogen-ion concentration in a solution 0.1 M in acetic acid and 0.1 Min potassium chloride. The calculated value is again 1.3 X. while the actual concentration of a difference of 30%. The difficulty is not with hydrogen ion is 1.7 X the law of mass action but with the fact that K, is not independent of the environment and is a tme constant only for a perfect solution (or more specifically, in this case, a solution containing no ions). In 0.1 M potassium chloride solution K, for acetic acid is 2.9 X lo-=. Even in dilute solutions of acetic acid Kc is not really constant, although the concentration of ions is very small. For example, the careful measurements of MacInnes and Shedlovsky (1)show that for a solution 0.000028 M in acetic acid Kc In and for a solution 0.0098 M ip acid Kc is 1.83 X is 1.76 X these solutions the ionic concentrations are 0.000015 and 0.00042 mole per liter, respectively. Now if the student is taughtvthat K, depends on the temperature, the medium, and the ionic concentration, he will not lose all his faith in the teacher later on. Another example of this sort will suffice. I will take a case of the common ion effect using benzoic acid as my example. The dissociation This constant of benzoic acid in aqueous solution a t 25' is 6.3 X 10". value is for a solution so dilute that there are no ions present; we might represent this dissociation constant by the symbol K,. For a solution 0.027 M in benzoic acid Kc is 6.6 X lo-', and we can calculate the hydrogenion concentration in the usual way. cHi2= 6.6 X 1 0 - 6 c ~ ~ .
If we make up a solution of benzoic acid containing sodium benzoate, it is not correct to calculate the hydrogen-ion concentration from the equation. ca+ = K.CHB/CB-
for K,. We must use that value which corusing the value 6.6 X responds to a solution containing sodium benzoate a t the particular con-
* Unless otherwise specified, for aqueous solutions ca+ will he used to represent the concentration of the hydrogen ion. HaO+.
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centration in question. For example, for a solution containing 0.011 mole of sodium benzoate per liter K, is 8.2 X The actual hydrogen-ion concentration of a sodium benzoate-benzoic acid buffer solution 0.011 M in sodium benzoate and 0.022 M in benzoic acid is 1.6 X rather than calculated on the assumption that K, remains constant. To 1.3 X illustrate further, K, for benzoic acid in potassium chloride solutions changes from 6.3 X a t zero ionic concentration to 10.1 X a t 0.1 M and continues to increase with increasing potassium chloride concentration up a t 3 M. to 0.6 M where K, is 11.3 X lo", it then decreases to 6.5 X A detailed discussion of the dissociation constant of benzoic acid, as well as comparison curves for other acids, is given in a recent publication (2). The change of K , with change in ionic concentration applies to all weak electrolyte equilibria and is even more marked when ions of higher valence are involved (3). Let us now turn to strong electrolytes. In the case of electrolytes such as sodium chloride, sodium hydroxide, and hydrochloric acid the student is usually taught either that the degree of dissociation can be determined from conductivity measurements, or that these substances are completely dissociated. The first is wrong and the second often misleading. Suppose that the student is taught that 0.1 M aqueous sodium chloride solution is 85% dissociated and that Kc is 0.49. These values are based upon the assumption that, since the equivalent conductance decreases with increasing concentration, the extent of dissociation decreases. We now know that the decrease in equivalent coqdnctance is due for the most part to decrease in the mobilities of the ions, from which it follows that the simple X/Xo ratio does not give the correct degree of dissociation. For a detailed treatment of this subject see the papers of Onsager (4). The other method is to start from the solid state and point out that in solid sodium chloride there are no molecules and consequently, since sodium chloride is completely ionized as a solid, i t is completely dissociated in solution. The argument is not a t all conclusive. It would not apply to the hydrogen halides. For a detailed discussion, the reader is referred to a paper by Jacobs and Eting (5). There is in fact a good deal of arbitrariness in what we mean by complete dissociation.* If the ions are so close that the interionic forces of attraction between oppositely charged ions are considerably greater than the kinetic energy, there may exist ion-pairs in the Bjerrum sense; these would act like molecules. A recent critical review of the problem points out that there is no physical property which is unquestionably due to undissociated molecules (6). What should we teach the student in order to leave him with an open mind? The author would point out that the older method of obtaining the
* The author would make a distinction between the terms complete ionization and complete dissociation.
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degree of dissociation is incorrect, and that the new view does not postulate 100% dissociation (7). All the evidence seems to indicate that uni-univalent strong electrolytes are practically completely dissociated in aqueous solution. At the present time we do not know their dissociation constants. The dissociation constants are certainly not as small as 0.5 in 0.1 M solution but on the other hand neither are they infinitely great. Estimates for hydrochloric acid place the dissociation constant a t lo6, corresponding to over 99% dissociation. Another difficulty which arises from lack of consideration of the effect of interionic forces is the teaching of solubility and solubility product in connection with analytical chemistry. The student is taught the solubility product relationship and is then asked to calculate the amount of precipitant necessary to effect practically 100% precipitation. In-all calculations the solubility product is assumed to remain constant. The result is that the student has fixed in his mind the idea that a large excess of the precipi+ = Ksp.,A B tant is always desirable. If he is precipitating AB, and c ~ CBthe more of B- added the more complete the precipitation of AB. Consequently he always tends to add an excess of B-. A good example of the change in solubility product with change in ionic concentration is furnished by the case of lanthanum iodate. One would expect, on the principle of the constancy of the solubility product, that lanthanum iodate would be less soluble in lanth3num nitrate solutions of increasing concentration. The data in the following table were obtained by La Mer and Gold@ man (8). TABLE I The Solubility of La(IO& in La(NO& Solutions Moles per Lit" La(NOda
0 0.001667 0.003333 0.01667 0.03333
La(IOda
0.0009482 0.0008347 0.0008101 0.0008696 0.WO9398
K s p . , La(I0a)r
2.184 X 3.926 X 5.944 X 3.113 X 7.672 X
10-'I 1OFL
lo-" 1OFo lo-"
At first the solubility decreases due to the common-ion effect, then it increases in spite of the common-ion effect. The reason for this is that the increase in the solubility product due to the increase in ionic concentration predominates over the decrease in solubility due t o the common-ion effect. The solubility product, which for an ionic concentration of zero is 7.6 X 10-l2 a t 25", increases with increasing ionic concentration as shown in column three of the table. In other words, if one were precipitating lanthanum iodate from a solution of iodate it would not be wise to add an excess of lanthanum nitrate greater than 0.003 mole per liter, for beyond that point the solubility increases. The change in the solubility product is
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quite general, and although it is not so marked with uni-univalent electrolytes, it nevertheless exists as shown by the careful measurements of Popoff and Newman (9) on the solubility of silver chloride in salt solutions. Again the question is-What shall we teach the student? The author would teach the student the solubility product principle but would not emphasize the constancy of K,. and would not have the student make detailed calculations assuming K,,. to be constant. Rather he would have him calculate the change of K,,, with change in ionic concentration, using the solubility data found in the literature. The discussion of the laws for the change of Kc and K,. with change in ionic concentration would then follow logically in his later courses. Literature Cited mSHEDLOVSKY, J. A m . Chen. Soc., 53, 2419 (1931). ( I ) MACINNES (2) CHASEnnm KXLPATRICK, ibid., 53, 2589 (1931). (3) BR~NSTED a m VOLQVARTZ, Z. physik. C h m . , 134,97 (1928); KILPATRICK, I. Am. Chem. Soc., 48, 2091 (1926). 4 ON~AGER, Physik. Z., 27, 388 (1926); 28, 277 (1927); Tmns. Faraday Soc., 23, 341 (1927). (5) JACOBS AND KIND,J. Phys. Chnn., 34,1923 (1930). (6) JACOBS nm, KING,ibid., 34, 1013-20, 1303-9 (1930); 35, 480-7, 192240 (1931). , jCr Electochem., 24, 321 (1918); Det. Kgl. Danskc Videnskeb. Sels(7) B p m u ~Z. No. 9 (1926). kab., Math-fys. M d d . , W, (8) LAMERAND GOLDMAN. 3. A m . Chem. +'oc., 51,2632 (1929). (9) POPOFF AND NEWMAN. I . P h y s Chem., 34,1853 (1930). C
