The Elements of Qualitative Chemical Analysis, vol. 1, parts 1 and 2. / With Special Consideration of the Application of the Laws of Equilibrium and of the Modern Theories of Solution.

by Julius Stieglitz

If we combine equations (2) and (3) we have

[H+] × [HCO3−] × [H+] × [CO32−]	= K1 × K2
([H2CO3] × [HCO3−])

(4)

or

[H⁺]² × [CO₃²⁻] / [H₂CO₃] = K.

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 acid[187] 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.