DECEMBER. 1951
8
COULOMB'S LAW AND THE QUALITATIVE INTERPRETATION OF REACTION RATES EDWARD S. AMIS University of Arkansas, Fayetteville, Arkansas
Tm following discussion is pertinent only when electrostatic influences upon ions in solution predominate over specific effects such as those arising from the solvent due to solvation (1) and other causes (2). Coulomb's law for ions in solution may be written for high dilution:
where F is the force between two ions of charges Zle and Za respectively, when the two ions are separated by a distance r in a medium of dielectric constant D. This
dielectric constant D can for all practical purposes, especially in dilute solutions, be identified with that of the pure solvent. The 2's represent the valencies of the ions and e is the electronic charge. The force F is attractive for ions of unlike sign but is repulsive for ions of like sign. Before we really use Coulomb's law for a qualitative interpretation of kinetic data we should have clearly in mind the Debye-Hiickel interionic attraction theory. The theory pictures an ion as being on a time average surrounded in a spherically symmetrical fashion by an atmosphere of ions of opposite charge to that of the central ion. This atmosphere would partially neutraliee the charge of the central ion with respect to its effect upon some ion outside the atmosphere. Now let us see what Coulomb's law would tell us about the effect upon ionic reaction rates of increasing the ion concentration of the solution a t constant dielectric constant and constant temperature. As ion con-
centration increases, the ion atmospheres surrounding any particular species of ion will become more dense. On the other hand, a t infinite dilution there would be no atmospheres surrounding any species of ion. Consider reactants of unlike charge so that the Coulomb force is an attractive one. The attractive force between the reactant ions a t high dilution would be given by equation (1). Now increase the ionic concentration by dissolving dissimilar ions in the solution. The reactant ions would begin to form atmospheres the density of which would depend on the total ion concentration in the solution. But when the atmosphere forms, the effective charge on the ion is lessened with respect to its influence on other ions. Thus the oppositely charged reactants will attract each other less strongly depending on the ion concentration in the solution. This can be seen from equation (I), for when Z,c and Zzc are diminished, the force F which is attractive in the case being considered becomes smaller a t constant D and r. Thus, from Coulomb's law, it can be predicted that when the total ion concentration is increased in a solution containing reactants of unlike sign, the attractive forces between the reactants will be lessened and their rate of reaction decreased. This result can be experimentally verified and quantitatively calculated using the ErGnsted-Debye equation (5). In the case of reactants of like charge the ion atmosphere effect will again be a decrease in the force hetween the reactants, hut in this case the force is repulsive, and by decreasing the repulsive force the ability
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of the reactants to contact each other is enhanced and their rate of reaction increased. The amount of increase will be a function of the amount of cancellation of charge, and therefore a function of the atmospheric density, and hence of the total ion concentration of the solution. Thus equation (1)would predict a lessening of repulsive forces with decreasing effective charge due t o ion atmosphere effects, and therefore would predict an increasing rate of reaction between reactants of like sign with increasing total ion concentration. This prediction can also be experimentally verified and the result can be calculated from the Br~nsted-Debye theory (3). Consider the effect upon the rate of ionic reactions of changing the dielectric constant of the solvent a t constant ionic strength and constant temperature. From Coulomb's law, if D is increased, other factors remaining constant, the force between ions becomes smaller. For ions of unlike sign the force is attractive and, as D increases, the attractive force decreases and the ionic reactants get together less readily; hence, the rate of reaction between such reactants would he decreased by raising the dielectric constant of the solvent. For ions of like sign the increased dielectric constant would cause a decrease in repulsive force and therefore ionic reactants of like sign would contact each other more readily and their rate of reaction would consequently he increased. When the dielectric constant of the medium is d e creased, the rates of reaction between ions of unlike sign would be increased due to increased attractive forces among the particles. For like charge of ionic reactants the rate of reaction would be reduced by decreasing the dielectric constant of the medium since the repulsive forces among the particles would be enhanced. All these effects have been exoerimentally verified (% 4 , 5 ) . The question might arise as to how the dielectric constant of a solvent can be controlled a t constant temperature. The answer is that mixed solvents can be used. Neither of the two solvents chosen must cause specific effects upon the rate. Thus a solvent of higher dielectric constant and a solvent of lower dielectric constant, the values of the dielectric constants of the mixtures of which, as a function of composition, have been recorded in the literature, are chosen. Several solvent pairs have been so studied (6, 7). Dioxane with a dielectric constant of approximately 2 and water with a dielectric constant of about 78 at ordinary temperatures is a favorite combination. The dioxanewater combination allows a wide variation of dielectric constant, the concentration variation of which over the range from 0 to 100 per cent of dioxane has been studied by Wymau (7) a t various temperatures. Furthermore dioxane is an inner ether, is inert t o many materials, and in adaition is soluble in water a t all proportions as is indicated by Wyman's dielectric constant studies. Thus, if one wants to decrease the
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dielectric constant in known amounts one calculates from Wyman's data the percentages of dioxane to put in the mixtures with water a t the temperature involved. Other mixtures for which data occur in the literature (6) include CHsOH-HeO, C2H60H-H20,acetone-HzO, and sucroseHzO. Suppose it is desired to decrease the rate of reaction, a t given temperature and concentration of reactants, between two ions of unlike sign such as NH4+ and CNO- which react to give ammonia. Then an indifferent salt, e. g., NaN03 could be added in accordance with the extent of lowered rate desired; also if methyl alcohol-water solvent is being used the proportion of water could he increased. The added salt would decrease the effective charge on the reactants thus decreasing the attractive Coulomb force and hence the rate. The increased amount of water would raise the dielectric constant of the medium thus decreasing the attractive Coulombic force and consequently lowering the rate of reaction. In the following table are summarized the predictions of Coulomb's law concerning the effects upon the rates of reaction between unlike signs of reactants and between like signs of reactants of changing ionic concentration and changing dielectric constant. Increase of total ion eancentration
Decrease of total ton mncentration
Increase o f dielkctric caslant
Decrease o f dielectric constant
Effect upon rate of Decrease reaction between unlike charge signs of reaEtants Effeot upon rate of Increase reaction between like oharee siens
Increase
Decrease
Increase
Decrease
Increase
Decrease
DEMONSTRATION
In giving a lecture demonstration, reactions that proceed fast enough to undergo perceptible change during the average lecture time of 50 minutes should be chosen. Reactions of greater rates are very desirable but slower ones cannot well he used. Further, it is best that the reactions used should be such that the rates of change are visually observable. It is not necessary that quantitative data be obtained in experiments designed to show how reaction rates can he increased or decreased by changing certain variables. Indeed in the short time of a lecture demonstration it would he difficult to obtain precise and accurate data even on reaction rates most amenable to the time allotted and to precision methods of measurement. In this lecture demonstration what is sought is s dramatic, easily observable, quick, qualitative demonstration of the points in question. For the above reasons two reactions are used t o illustrate the points brought out in the theoretical discussion. The effect of dielectric constant of the
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DECEMBER. 1951
medium can be demonstrated in the following way, using the reaction between the negative bivalent tetrabromophenolsulfonphthalein ion and the negative hydroxyl ion to give the colorless carbinol (6). The reaction is thus between ions of like charge sign and the rate should be slowed down by decreasing the dielectric constant of the solvent. At a given temperature the dielectric constants of water-ethyl alcohol mixtures are lower than that of water depending on the proportion of alcohol. We shall therefore choose such a concentration of alcohol as to change the dielectric constant and hence the rate of the fading reaction appreciably. Such concentrations of reactants will be used that the difference in rates in pure water and in water-alcohol solvents are readily observable within the 50-minute lecture period. Prepare two solutions simultaneously. Solution 1 is prepared by pipetting into a 100-ml. volumetric flask 10 ml. of m-tetrabromophenolsu1fonphthalein, 50 ml. of 3 N sodium hydroxide, and 25 ml. of ethyl alcohol, and diluting to the mark. Solution 2 is prepared by pipetting into a 100-ml. m-tetrabromophenolsulvolumetric flask 10 ml. of fonphthalein and 50 ml. of 3 N sodium hydroxide, and diluting to the mark. Both solutions are mixed well by inverting the flasks several times and the flasks are then set on the lecture desk for observation. It will be observed that within a period of 30 minutes or so the dye in the pure water (dielectric constant 78.5 a t 25°C.) will be almost completely faded. The dye in water-ethyl alcohol mixture (dielectric constant about 67 a t 25°C.) will not have faded appreciably but, on stand'mg 12 to 15 hours, will be decolorized. By reducing the proportion of alcohol in the mixed solvent the difference in fading rate in water and water-alcohol solvents can be reduced. The above reaction cannot be used to demonstrate the salt effect satisfactorily because a t the high concentration of sodium hydroxide used for short fading time the ionic strenhh effect has vracticallv reached its limiting value and further addition of sali does not have a marked effect. A reaction which is amenable to the demonstration of the salt effect is the iodine clock reaction (8). The slow rate-controlling step in this reaction is the oxidation of the sulfite ion by iodate ion to the sulfate ion. The iodate ion is reduced to iodide ion which, when all the sulfite ion is used up, is oxidized by excess iodate ion t o yield iodine. The iodine with starch gives starch-iodide blue. Therefore, as soon as all of the sulfite ion is used up, the solution which contains starch instantly turns blue. The controlling step of the reaction is again between ions of like charge
sign and the rate should increase with increased ionic strength. Prepare two solutions. Solution 1 contains 2.0 g. of potassium iodate per liter of water solution. Solution 2 contains 0.40 g. of sodium bisulfite and 5.0 ml. of 1.0 M sulfuric acid per liter of water solution. Prepare also a saturated solution of sodium chloride. Into a beaker of convenient size measure 20 ml, of water. Into one 10-ml. graduate measure 10 ml. of solution 1 and into another like graduate measure 10 ml. of solution 2. Invert simultaneously the two 10-ml. graduates containing the two solutions over the beaker containing the 20 ml. of water and note the time (or start a stop watch). Allow the graduates to drain for five seconds and mix the contents of the beaker well by giving the beaker a swirling motion with the hand. I n about 140 seconds the solution will instantly become blue in color. Time the appearance of the blue color (stop the stop watch). Now measure into a clean beaker 10 ml. of water and 10 ml. of saturated sodium chloride solution. Again add simultaneously 10 ml. each of solutions 1 and 2 from graduates and time as before. The blue color will now appear in about 5 8 4 seconds. If the 20 ml. of water is replaced entirely by 20 ml. of saturated salt solution and the rest of the experiment is carried out identically as above the time of appearance of the blue color will be reduced to about 20 seconds. The iodine clock reaction is not well adapted to the study of dielectric constant effects in mixed solvents because all common solvents other than water are chemically active with the reagents of the reaction. Thus dioxane and acetone react with and decolorize starch-iodide blue so that there is no blue color formed when either of these solvents constitutes one component of the mixed solvent. Ethyl alcohol and methyl alcohol affect the starch. For example, when the mixed solvent is 50 per cent by volume ethyl or methyl alcohol the starch visibly forms larger aggregates and in ethvl alcohol is nreci~itatedin strine-like fluffs.
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LITERATURE CITED (1) VERFIOEK, F. H., J.Arn. Chem. Soe., 61,186 (1939). (2)
AMIS, E. S., "Kinetics of Chemical Change in Solution,"
The Maomillan Co., NewYork, 1949, Chap. IX. (3) LAMER, V. K., Chem. Rev., 10,179 (1932). (4) h s , E. S., AND J. B.PRICE, J. Phys. Chem., 47,338 (1944). (5) Ahars, E. S., AND V. K. LA MER,J. A m . Chem. Soc., 61 905 (1939). (6) HKERLBF, G., ibid., 54,4125 (1932). (7) WYMAN, W., JR.,ibid., 58,1482 (1936). (8) FOSTER, W., AND H. N. ALYEA,"An Introduction to General Chemistry," 3rd ed., D. Van Nostrand Co., Inc., New
York,p. 255.
