At 440°, the results given in the following table were obtained by Bodenstein. The concentrations are expressed in moles per liter.173 The constant is calcuated according to the equation just given. Analytical errors affect the value of the constant most in the first and last experiments, as a result of the very small concentrations of one component, I2 or H2. [p095]
| [H2] | [I2] | [HI] | K |
|---|---|---|---|
| 0.0268 | 0.000190 | 0.0177 | (0.016) |
| 0.00986 | 0.00203 | 0.0328 | 0.019 |
| 0.00308 | 0.00783 | 0.0337 | 0.021 |
| 0.00175 | 0.0114 | 0.0315 | 0.020 |
| 0.000653 | 0.0204 | 0.0236 | 0.024 |
| 0.000265 | 0.0242 | 0.0202 | (0.016) |
The mechanical significance of the raised powers of the concentrations of components, two or more molecules of which take part in a reaction as indicated, will be discussed further on, in connection with a case of equilibrium between an electrolyte and its ions (Chapter VI, p. 102).
The following experiments may be used to illustrate the significance of the two classes of factors: Phosphorus pentabromide is partially decomposed by heat into the tribromide and bromine (a case of gaseous dissociation):
Phosphorus trichlordibromide is decomposed more or less, in a similar fashion, into the components phosphorus trichloride and bromine, according to the equation
For the condition of equilibrium in the two cases we have
Exp. Two tubes containing equivalent quantities of the two bromides are placed side by side in warm water.178 The tube containing the trichlordibromide is found to be much more intensely colored by free bromine than that containing the pentabromide.
The intensity of the color of the bromine vapor shows that the concentration of bromine, [Br2]″, in the PCl3Br2 tube, is greater than the corresponding concentration, [Br2]′, in the PBr5 tube. As a molecule of pentahalide PX5 dissociates into one molecule of PX3 and one molecule of X2, [PCl3] equals [Br2]″ and is greater than [PBr3], which is equal to [Br2]′. Further, more of the pentabromide than of the trichlordibromide must be left undecomposed, i.e. [PCl3Br2] is smaller than PBr5. Since the factors in the numerator of the second equation are both larger, and the factor in the denominator smaller, than the corresponding factors in the first equation, k2 must be greater than k1. These constants are thus seen to be a measure of the chemical stability of these pentahalides. It is evident, too, that in reactions which depend on the presence of free bromine, such as the bromination of many organic compounds, the trichlordibromide should be more effective than the equivalent quantity of the pentabromide. [p097]
In the second place, if we were to introduce into either tube, for instance into the tube containing the phosphorus trichlordibromide, an excess of one of the dissociation products, say an excess of phosphorus trichloride, then the condition of equilibrium would necessarily be disturbed:
in which the bracketed symbols represent the concentrations of the first experiment. The velocities of the two opposite reactions would be no longer equal, the combination of trichloride with bromine would be accelerated by the increased concentration of the former. Here, equilibrium would only be reëstablished when the trichloride and bromine had combined to a sufficient extent to make
| (y [PCl3] − x) × ([Br2]′ − x) | = k2, |
| ([PCl3Br2] + x) |
in which x represents the number of moles of additional phosphorus trichlordibromide formed in unit volume by the combination of bromine with phosphorus trichloride. The net result is seen to be that an increase in the concentration of the one dissociation product eo ipso reduces the concentration of the other dissociation product.
Exp. A third tube charged with the same quantity of phosphorus trichlordibromide as the tube mentioned above, and with an added excess of phosphorus trichloride, is placed in the warm water next to the tube containing the trichlordibromide. Its color is much paler than that of the latter, owing to the suppression of free bromine.179
The concentration of the free bromine, ([Br2]′ − x), under the new conditions of equilibrium, is smaller than the original concentration [Br2]′—a result confirmed by experience. It is in our power, therefore, arbitrarily to change the concentration of a reacting component, in a case of equilibrium, and thus to affect the reactivity of the system; for instance, for brominating purposes, the new system would be less effective than the original one, and it might be of especial service where bromination is to be avoided.
In the cases studied, are found the two fundamentally important relations expressed by the law of equilibrium: the equilibrium constant is a measure of the stability of a certain system and, in a way, of its reactivity at a given temperature; and the [p098] concentration factors are variables, which we may change to a very considerable extent, so as, to a certain degree, to subject the system to our own purposes. We shall repeatedly have occasion to refer to these two fundamental relations and we shall use them again and again in our analytical work.
If the total concentration of the acid is known, the concentrations of the ions and of the non-ionized acid may be calculated from the conductivity of the solution. For instance, if 60 grams of acetic acid (1 mole) is dissolved in sufficient water to make 10 liters, the equivalent conductivity of the solution (p. 50) is found to be 4.67 reciprocal ohms at 18°. The maximum conductivity of one mole of acetic acid, at infinite dilution, when all the acid would be ionized, would be 347. Therefore, in the acid under examination, 4.67 / 347, or 1.34 per cent, is ionized (p. 50). Since the total concentration of the acid is 0.1 mole per liter and 1.34 per cent is ionized, the concentration of the hydrogen-ion, [H+], is 0.1 × 0.0134, and that of the acetate-ion, [CH3CO2−], is the same. The concentration of the non-ionized acetic acid, [CH3CO2H], is 0.1 × 0.9866. If these values are inserted in the equation for the condition of equilibrium, we have
| (0.1 × 0.0134)2 | = Kionization = 18.2E−6. |
| 0.1 × 0.9866 |
From this experimental result, the equilibrium constant, which is called the ionization constant of the acid, is found to have the value 18.2E−6. If the ratio [H+] × [CH3CO2−] / [CH3CO2H] really is a constant, the same value, within the limits of experimental errors, should be obtained from acetic acid in other concentrations. Now, if the above solution is diluted to ten times its volume, the concentration of the acid is made 0.01 mole per liter, the conductivity [p099] is found to have increased to 14.5 reciprocal ohms, and the percentage of ionized acid is then 14.5 / 347, or 4.17. Here, [H+] and [CH3CO2−] = 0.01 × 0.0417 and [CH3CO2H] = 0.01 × 0.9583. Inserting these values in our general equation and calculating the result, we obtain 18.1E−6 as the value of the constant. In the following table180 are given the molar conductivities, Λ (column 2), of acetic acid of varying concentrations, m (column 1). The degrees of ionization, α, and the ionization constant, calculated according to the equilibrium equation, are given in columns 3 and 4.
Ionization of Acetic Acid. Λ∞ = 347.
| m. | Λ. | 100 α. | K. |
|---|---|---|---|
| 0.1 | 4.67 | 1.34 | 18.2E−6 |
| 0.08 | 5.22 | 1.50 | 18.3E−6 |
| 0.03 | 8.50 | 2.45 | 18.5E−6 |
| 0.01 | 14.50 | 4.17 | 18.1E−6 |
It is evident, that a constant value is found for the ratio [H+] × [CH3CO2−] / [CH3CO2H] and that the ionization of acetic acid, in these dilute solutions, obeys the law of chemical equilibrium.181 The equilibrium constant expresses in definite, quantitative terms the tendency of acetic acid to ionize in dilute solution. Examination of other acids shows that there is an enormous range in the values found for their respective ionization constants. The constants are the best measure of the strength of the acids as acids. Obviously, the more readily acids in equivalent solutions ionize, the greater will be the concentration of the hydrogen-ion to which the characteristic acid properties are due, and the more pronounced (stronger) will be the exhibition of these properties. From the ionization constants one may calculate, for instance, the proportion in which two competing acids will neutralize a base, when the latter is used in quantity insufficient to neutralize both acids. [p100]
Inspection of the equation for acetic acid, which is the typical equilibrium equation for all monobasic acids, shows that the greater the degrees of ionization of acids are in equivalent solutions, i.e. the greater the concentrations of the hydrogen-ion which their ionization produces in equivalent solutions, the larger will be the values of their ionization constants. The acids with the larger constants are, then, the stronger acids.
In the first place, for the strongest acids, such as hydrochloric, nitric, hydrobromic and similar acids, chemists have been unable to determine ionization constants on the basis of the law of chemical equilibrium. Strong acids, strong bases and most salts (see pp. 106–8, below), the three classes comprising all the very readily ionizable electrolytes, do not give constants when the values of the equilibrium ratio,182 [Cation] × [Anion] / [Molecules], are calculated for different concentrations, and they therefore do not ionize simply in accordance with the law of chemical equilibrium. The reasons for this abnormal behavior will be discussed presently (p. 108), when other necessary facts are before us. In order to have, at least, a rough basis for comparison of these strong acids with the weak ones, which do obey the law of chemical equilibrium, the table will give for the strong acids the value of the above ratio as calculated from their ionization in 0.1 molar solutions.
We may ask, however, whether both the hydrogen atoms of carbonic acid show the same tendency to ionize, or, since there is a vast difference in the ease of ionization of different acids, whether there is not also a difference in the ease of ionization of the different hydrogen atoms in a polybasic acid. As a matter of experiment, we find that a molecule of carbonic acid does ionize, first, and more readily, into one hydrogen ion and an acid carbonate ion HCO3−, according to H2CO3 ⇄ H+ + HCO3−.
For this reversible reaction we have184
The value of this constant,185 called the primary ionization constant of carbonic acid, is 0.3E−6.
The acid carbonate-ion HCO3−, in turn, is ionized to a certain extent, producing another hydrogen ion and the carbonate-ion, CO32−. We have HCO3− ⇄ H+ + CO32−, and
The value of this constant186, called the constant of the [p102] secondary ionization of carbonic acid, is 0.07E−9, which has about one four-thousandth of the value of the constant for the primary ionization.
If we combine equations (2) and (3) we have
| [H+] × [HCO3−] × [H+] × [CO32−] | = K1 × K2 |
| ([H2CO3] × [HCO3−]) |
or
This is equation (1), derived originally by the application of the law of mass action to the relation between the carbonate-ion, CO32−, the hydrogen-ion, and carbonic acid, H2CO3.
This relation, and, in particular, the significant squaring of the concentration of the hydrogen-ion, an ion which appears twice in the equation for the formation of carbonic acid from carbonate and hydrogen ions, (2 H+ + CO32− ⇄ H2CO3), may now be interpreted mechanically (p. 92) as follows: For the formation of carbonic acid from a carbonate ion and two hydrogen ions, a carbonate ion must collide and combine first with one hydrogen ion, and the velocity for the formation of this intermediate product, HCO3−, will be proportional to the (total) concentration of the hydrogen ions; the product, HCO3−, to form H2CO3, must collide and combine with a hydrogen ion once more, and this combination will proceed with a velocity again proportional to the (total) concentration of the hydrogen ions. So the velocity for the transformation of CO32− into H2CO3 will be proportional twice over to the (total) concentration of the hydrogen ions—as well as, in the usual fashion, to the concentration of the carbonate ions present at any moment.
It is a general principle that the primary ionization of polyvalent acids occurs more readily than the secondary, and this in turn more readily than the tertiary (if a third ionizable hydrogen atom is present in the acid).
In the case of phosphoric acid, for instance, the primary ionization into the hydrogen-ion and the dihydrogen-phosphate-ion, H2PO4−, takes place so readily that phosphoric acid reacts strongly acid187 to methyl orange,188 the [p103] concentration of hydrogen-ion being sufficiently great to affect this indicator (see Exp. below).
When phosphoric acid is neutralized by one equivalent of a base, say of sodium hydroxide, the salt formed, sodium dihydrogen-phosphate, NaH2PO4, yields sodium-ion and dihydrogen-phosphate-ion, H2PO4−. The latter is ionized somewhat into H+ and the bivalent hydrogen-phosphate-ion, HPO42−. The ionization of the ion H2PO4− is now the chief source of supply of hydrogen-ion (the further ionization of HPO42− is practically negligible here) and it is ionized so little that the solution of NaH2PO4 no longer changes the color of methyl orange (see Exp. below). The solution is, however, acid to the indicator phenolphthaleïn, which is much more sensitive to the hydrogen-ion and will show the presence of much smaller concentrations of it than will methyl orange. The addition of a second equivalent of sodium hydroxide to the solution converts NaH2PO4 into Na2HPO4. This salt gives sodium-ion and the hydrogen-phosphate-ion HPO42−, which, in turn, is ionized only very slightly, producing phosphate-ion PO43−, and again hydrogen-ion. The ionization of HPO42− is so slight, however, and the concentration of the hydrogen-ion, therefore, so minute, that the solution does not react acid even to the sensitive indicator phenolphthaleïn.
Exp. Methyl orange (very little) is added to 10 c.c. of a 0.1 molar solution of phosphoric acid and 10 c.c. of 0.1 molar sodium hydroxide solution is added to the mixture; the color will be found to change from the acid to the neutral tint just as the last drop or two of the alkali are added. Phenolphthaleïn is then added to the mixture and 10 c.c. more of the 0.1 molar sodium hydroxide solution are required to change the color of the mixture to a pronounced pink (alkaline) tint.
Even sulphuric acid, although its two hydrogen atoms are ionized very easily, making sulphuric acid a strong acid, shows a difference in the ease of ionization of the two hydrogen atoms. Since ionization, in general, is favored by dilution, we find that in the case of such a strong acid the difference is most marked in more concentrated solutions, the smaller amount of water starting the ionization in the more favored direction and producing first, chiefly, hydrogen-sulphate ions, HSO4−. When the solution is diluted, the hydrogen-sulphate ions are to a very considerable extent dissociated into sulphate ions and hydrogen ions. The described change in ionization can be roughly followed with the aid of an insoluble sulphate like barium sulphate. Barium sulphate, while very insoluble in water, dissolves in rather strong sulphuric acid to form the acid sulphate, Ba(HSO4)2, the SO42− ion of the sulphate being more or less suppressed by uniting with hydrogen-ion. We have the action
If the solution of the acid sulphate is poured into a large volume of water, barium sulphate is immediately reprecipitated, the hydrogen-sulphate-ion being dissociated, in the dilute solution, into hydrogen-ion and sulphate-ion, SO42−, whose barium salt is so difficultly soluble:
Exp. Finely divided barium sulphate is warmed for a moment with a few cubic centimeters of concentrated sulphuric acid in a test tube, the mixture is allowed to settle, and some of the clear acid is carefully decanted into a large beaker full of water.
It may be added, that while the primary ionization of sulphuric acid does not yield an equilibrium constant for the ratio [H+] × [HSO4] / [H2SO4], even such a strong acid as is sulphuric acid is found to give a fairly good constant189 for [H+] × [SO42−] / [HSO4−]. The value of this constant189 is 0.03.
The Ionization ConstantsA of Acids
| Acid. | Equilibrium Ratio. | K. |
|---|---|---|
| Hydrochloric | [H+]×[Cl−]/[HCl] | (1) |
| Hydrobromic | [H+]×[Br−]/[HBr] | (1) |
| Hydroiodic | [H+]×[I−]/[HI] | (1) |
| Nitric | [H+]×[NO3−]/[HNO3] | (1) |
| ChromicB | [H+]×[HCrO4−]/[H2CrO4] | (1) |
| [H+]×[CrO42−]/[HCrO4−] | 0.6E−6 | |
| SulphuricC,D | [H+]×[HSO4−]/[H2SO4] | (1) |
| [H+]×[SO42−]/[HSO4−] | 0.3E−1 | |
| OxalicE | [H+]×[C2O4−]/[H2C2O4] | 3.8E−2 |
| [H+]×[C2O42−]/[HC2O4−] | 0.5E−4 | |
| PhosphoricF | [H+]×[H2PO4−]/[H3PO4] | 0.1E−1 |
| [H+]×[HPO42−]/[H2PO4−] | 0.2E−6 | |
| [H+]×[PO43−]/[HPO42−] | 0.4E−12 | |
| ArsenicD | [H+]×[H2AsO4−]/[H3AsO4] | 0.5E−2 |
| NitrousB | [H+]×[NO2−]/[HNO2] | 0.5E−3 |
| AceticG | [H+]×[CH3CO2−]/[CH3CO2H] | 1.8E−5 |
| CarbonicH,I | [H+]×[HCO3−]/([H2CO3]+[CO2]) | 0.3E−6 |
| [H+]×[CO32−]/[HCO3−] | 0.7E−10 | |
| Hydrogen SulphideJ,K |
[H+]×[SH−]/[H2S] | 0.9E−7 |
| [H+]×[S2−]/[SH−] | 0.1E−14 | |
| BoricB | [H+]×[H2BO3−]/[H3BO3] | 0.7E−9 |
| Hydrocyanic | [H+]×[CN−]/[HCN] | 0.7E−9 |
| Arsenious | [H+]×[H2AsO3−]/[H3AsO3] | 0.6E−9 |
| WaterL,C | [H+]×[HO−]/[H2O] at 25° | 0.2E−15 |
| at 100° | 0.9E−14 | |
| [H+]×[HO−] at 25° | 1.2E−14 | |
| at 100° | 0.5E−11 |
[A] As explained on p. 100, the bracketed values given for the strong acids are not constants, but express the values of the ratios [H+] × [Anion] / [Acid] for 0.1 molar solutions.
[B] See references, Noyes, ibid., 32, 860 (1910).
[C] Noyes and Eastman, Carnegie Institution Publications, 63, 274 (1907).
[D] Luther, Z. Elektroch, 13, 296 (1907).
[E] Chandler (McCoy), J. Am. Chem. Soc., 30, 713 (1908).
[F] Abbot and Bray, ibid., 31, 760 (1909).
[H] Walker, J. Chem. Soc., (London), 77, 5 (1900).
[I] McCoy, Am. Chem. J., 29, 455 (1903); Stieglitz, Carnegie Institution Publications, 107, 243 (1909).
[J] Auerbach, Z. phys. Chem., 49, 220 (1904).
[K] Knox, in Abegg's laboratory, Trans. Faraday Soc., 4, 43 (1908).
The difference in the tendencies of acids to ionize, as expressed in the table, may be recognized in equivalent solutions by any of the properties dependent on the ionization, such as the conductivity, the chemical activity, the osmotic pressure and allied effects, and so forth. If the conductivities of equal volumes of equivalent (e.g. normal) solutions of hydrochloric, phosphoric and acetic acids are compared (exp.)190, it is readily seen that hydrochloric acid is the best conductor, phosphoric acid a much poorer one, and acetic acid an exceedingly poor one (the conductivity of normal acetic acid is about 1 / 200 that of normal hydrochloric acid, and the conductivity of normal phosphoric acid is about 1 / 14 that of normal hydrochloric acid). Since the conductivity is approximately proportional to the concentration of the hydrogen-ion191 in each of the solutions, it is evident that the hydrochloric acid is ionized to a considerably greater extent than either of the other acids—than acetic acid, in particular. Similarly, if a drop (0.05 c.c.) of molar hydrochloric acid and a drop of molar acetic acid are added to equal volumes (50 c.c.) of a very dilute solution of methyl orange (exp.), the color will be changed decidedly by the hydrochloric acid to a bright pink, but by the acetic acid only to an orange hue. Again, if a precipitate of barium chromate or calcium oxalate is treated with some strong acid, hydrochloric or nitric, for instance, it dissolves readily, while a considerable excess of acetic acid (exp.) only dissolves traces of either precipitate.192 In this way, the chemical behavior of these acids differs in degree, as a result of the different tendencies to ionize, which are expressed in the constants of the table. Advantage is taken, in analysis, of such differences. Acetic acid, for instance, is used when only a slight degree of acidity is desired—as in recognizing barium-ion by its chromate, or oxalic acid by means of its calcium salt. Hydrochloric or nitric acid is used when decided acidity is required—as in the separation of groups by hydrogen sulphide (Chap. XI).
The Ionization ConstantsA of Bases
| Base. | Ratio. | K. |
|---|---|---|
| Potassium hydroxide | [K+]×[HO−]/[KOH] | (1) |
| Sodium hydroxide | [Na+]×[HO−]/[NaOH] | (1) |
| Barium hydroxide | [Ba2+]×[HO−]2/[Ba(OH)2] | (0.03) |
| Strontium hydroxide | [Sr2+]×[HO−]2/[Sr(OH)2] | (0.03) |
| Calcium hydroxideB | [Ca2+]×[HO−]2/[Ca(OH)2] | (0.03) |
| Ammonium hydroxideC,D | [NH4+]×[HO−]/([NH4OH]+[NH3]) | 1.8E−5 |
| HydrazineE | [N2H5+]×[HO−]/([N2H5OH]+[N2H4]) | 0.3E−5 |
| AnilineF | [C6H5NH3+]×[HO−]/ ([C6H5NH3OH]+[C6H5NH2]) |
0.5E−9 |
| Water | [H+]×[HO−]/[H2O] at 25° | 0.2E−15 |
| at 100° | 0.9E−14 | |
| [H+]×[HO−] at 25° | 1.2E−14 | |
| at 100° | 0.5E−11 |