Part 1 — CHAPTER VI CHEMICAL EQUILIBRIUM. THE LAW OF MASS ACTION

[p090] TOC

The theory of ionization, as studied so far, gives us simple, rational explanations of many of our qualitative reactions—explanations which agree with phenomena taken from separate fields of investigation. But, if our study of the theory ceased at the present stage without further elaboration, we should fail to find in it a satisfactory explanation of a number of other important facts of analysis—notably, why certain reactions, the occurrence of which we might anticipate, do not take place. For instance, the addition of a soluble carbonate to a barium chloride solution precipitates almost all the barium as barium carbonate (exp.); we have 2 Na⁺ + CO₃²⁻ + Ba²⁺ + 2 Cl⁻ → BaCO₃ ↓ + 2 Na⁺ + 2 Cl⁻. But the addition of carbonic acid to barium chloride solutions fails to produce the slightest precipitate (exp.), although carbonic acid also gives rise to the carbonate-ion, CO₃²⁻. In the same way silver nitrate readily precipitates silver phosphate from sodium phosphate solutions (exp.), but not from a solution of phosphoric acid (exp.). Hydrogen sulphide precipitates zinc sulphide from a zinc sulphate solution (exp.), Zn²⁺ + SO₄²⁻ + 2 H⁺ + S²⁻ → ZnS ↓ + 2 H⁺ + SO₄²⁻; but the addition of hydrochloric acid effectually prevents the precipitation (exp.), although the hydrogen sulphide is still ionized, as is apparent from the precipitation of copper sulphide when copper sulphate is added to the mixture (exp.). In the negative results, we have instances of a very large number of cases which require closer study, and a further development of the theory, if we wish to interpret them satisfactorily. The line of development to be followed is indicated perhaps most sharply by the following experiment.

Exp. Some sodium tetraborate (borax) is dissolved in a little water and silver nitrate is added to a small part of the solution. A pure white precipitate (silver borate) results. Another portion of the borate solution is diluted with a large quantity of water, and then silver nitrate is added; quite a different result is obtained—a brown precipitate (silver oxide) is formed. [p091]

The change in the quantity of water brought about the difference in result—the quantitative relations were altered thereby. In order to follow intelligently this and the other actions referred to, the study of reactions in solutions must be taken up from the quantitative side—the development heretofore has been essentially qualitative in character. On several occasions we have found that all electrolytes do not ionize equally well, and that the intensity of their action, demonstrated, for instance, for potassium and ammonium hydroxides, varies accordingly. We shall now have to study these relations in greater detail.

For our purpose, the study of two of the fundamental quantitative laws governing action in solution and of their application to analytical phenomena, will be sufficient: these are, the law of chemical or homogeneous equilibrium, in which the law of mass action is included, and the law of physical or heterogeneous equilibrium.

The Law of Chemical Equilibrium.

—The law of chemical equilibrium may be expressed, for a simple case, by saying that if two substances

A

and

B

interact at a constant temperature to give two compounds

C

and

D

and, vice versa,

C

and

D

interact with each other to produce

A

and

B

, then equilibrium will be reached

when the ratio of the product of the concentrations of

A

and of

B

to the product of the concentrations of

C

and of

D

has a definite, constant value

, which is a value characteristic of the equilibrium between the compounds involved, at the given temperature. The action may be expressed in the chemical equation

A + B ⇄ C + D,

in which A, B, C and D represent four different substances reacting in the molecular proportions indicated by their symbols, which as usual represent molecular weights. And the condition for equilibrium may be expressed in the mathematical equation

[A] × [B] / ([C] × [D]) = k.

[A], [B], [C] and [D] are used to represent the concentrations166 of [p092] the four reacting substances and k is some definite number, called the equilibrium constant.

The law was discovered by Guldberg and Waage in 1867, and, with certain limiting conditions (see below) it has been fully established by extensive experimental work.167 The significance of the law may be interpreted on the basis of the following considerations. If we start with the two substances A and B alone and have one mole of each in one liter (as gas or in solution) at a given temperature, then, all the conditions being given,—the temperature, the concentrations, and the nature of the substances,—the reaction A + B → C + D, leading to the formation of C and D, will proceed with a perfectly definite velocity. The molecules of A and of B move in all directions (kinetic theory of gases and solutions), and molecules of A will collide with molecules of B a definite number of times in unit time and will form a definite number168 of molecules of C and D per minute. The velocity of chemical change of a given substance (chemical velocity) is also measured in terms of moles, and is represented by the number of moles or the fraction of a mole changed per minute. If v′₁ stands for the velocity of the action between A and B, under the given conditions, then

v′₁ = k₁,

where k₁ is some number. Now, if the concentration of one of the components, e.g. A, should be doubled, then the chances for collision and for action between molecules of A and B will be twice as great as before and the velocity of the action will be doubled. If only one-tenth of the concentration of A (one-tenth mole) is used, the velocity will only be one-tenth as great as originally, and, in general terms, if [A] moles of A are used per liter, the velocity of the change will be proportional to [A], and equal to k₁ × [A]. If the concentration of the other reacting component, B, is now doubled, the chances for action are again doubled, and, in general, the velocity of the action will be proportional also to the concentration [p093] [B] of the second reacting substance. For the velocity, v₁ of the action for any concentrations, [A] and [B], of A and B at any moment at a given temperature, we have

v₁ = k₁ × [A] × [B].

Hence, if by the symbols [A] and [B] the concentrations at any given moment are represented, we may say that the velocity of the formation of C and D at that moment169 is proportional to the product of the concentrations of A and B, and to some constant, which is characteristic of the interaction of A and B.

The validity of this conclusion has been fully verified by experiment.170 The case is an instance of the law of mass action, which states that in chemical changes the velocity of the action is proportional at any moment to the molecular concentrations171 of the reacting components, and to a constant, which is characteristic of the chemical nature of the reacting components (and of the temperature).

If we start with the reversed action

A + B ← C + D,

the relation may be developed in the same way. Thus the two substances C and D will react upon each other, at the given temperature, with a velocity proportional to a constant, k₂, and, at any given moment, proportional also to their respective concentrations at that moment:

v₂ = k₂ × [C] × [D].

Equilibrium will be reached when the substances A and B are formed at any moment from C and D just as rapidly as they are used up to produce C and D, and vice versa. Such is the case, [p094] when the velocities of the two opposite reactions are equal to each other. For the condition of equilibrium, then, v₁ must be equal to v₂ and therefore

k₁ × [A] × [B] = k₂ × [C] × [D]

or

[A] × [B] / ([C] × [D]) = k₂ / k₁ = k_equilibrium.

In this way the meaning of the fundamental law of chemical equilibrium may be developed from the consideration of the velocities of the reversible actions, such as are involved in all conditions of equilibrium, and the equilibrium constant represents the ratio of the velocity constants of the two opposite reactions. This conclusion has been fully verified by experiment, the equilibrium constant being, as a matter of fact, found equal to the ratio of the velocity constants.172

The relations, so far considered, have been those of the simplest type of reversible reaction. We may now discuss the modifications required for other types of reaction by the law of equilibrium.

When two molecules of any reacting component take part in a reaction—for instance, in A + 2 B ⇄ C + D—the concentration of this component is raised to the second power in the mathematical expression of the law of equilibrium; when three molecules of a component take part, its concentration is raised to the third power, etc.

For instance, hydrogen iodide is decomposed, reversibly, into hydrogen and iodine, according to 2 HI ⇄ H₂ + I₂. A condition of equilibrium is reached, at a given temperature when

[H₂] × [I₂] / [HI]² = K.

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).

Limitations to the Law of Chemical Equilibrium.

—Quite in agreement with the interpretation of the law of chemical equilibrium from the view-point of the kinetic theory, it is found that, in its applications, one must take into consideration the possibility, that molecular attractions (p.

27

) or other important forces of attraction or repulsion (

e.g.

electrical) of a more than

negligible

magnitude exist between the molecules of the components in a reversible reaction. If such forces are involved, suitable allowance must be made for them, so that the mathematical formulation of the law may express the facts of observation.

174

For these reasons, the law, in its simplest terms, which, alone, can be considered here, holds for the relations

obtaining in dilute systems

175

(dilute solutions or gases that are not too strongly compressed), and in

systems involving only nonelectrolytes or only weak ionogens

, more generally than for the relations in concentrated solutions (or strongly compressed gases) or in systems, in which electrically charged particles (ions) are present in large proportions (see below, p.

108

).

The Factors of the Law of Chemical Equilibrium.

—Inspection of the mathematical expression of the law of chemical equilibrium (p.

91

) shows that there are two significant kinds of factors in it: first, the equilibrium

constant

, whose value depends only on the nature of the substances involved and on the temperature.

176

In

[p096]

the second place, we have concentration factors, which, to a large extent,

177

may be varied at will.

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):

PBr₅ ⇄ PBr₃ + Br₂.

Phosphorus trichlordibromide is decomposed more or less, in a similar fashion, into the components phosphorus trichloride and bromine, according to the equation

PCl₃Br₂ ⇄ PCl₃ + Br₂.

For the condition of equilibrium in the two cases we have

[PBr₃] × [Br₂]′ / [PBr₅] = k₁ and [PCl₃] × [Br₂]″ / [PCl₃Br₂] = k₂.

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:

y [PCl₃] × [Br₂]′ / [PCl₃Br₂] > k₂,

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.

Chemical Equilibrium of Electrolytes.

—Ionization of an electrolyte is a reversible chemical action and its relation to the law of chemical equilibrium will now be discussed. For acetic acid, ionization into hydrogen and acetate ions occurs thus:

CH

3

CO

2

H ⇄

CH

3

CO

2

−

+ H

+

,

and, in accordance with the law of equilibrium, at a given temperature, the following relation would hold:

[H⁺] × [CH₃CO₂⁻] / [CH₃CO₂H] = K_ionization.

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 = K_ionization = 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.

The Ionization of Various Acids.

—The table given on page

104

shows the ionization constants for a number of acids of interest in analysis. Before proceeding to give the table, we must consider further two important points.

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.

The Ionization of Polybasic Acids.

—In the second place, the meaning of the

constants for polybasic acids

, such as sulphuric, phosphoric, carbonic and similar acids, requires explanation. The relations for carbonic acid will be first developed, as representing a typical case. Carbonic acid, in ionizing, forms the carbonate-ion CO

3

2−

, and the hydrogen-ion, as expressed in the

[p101]

equation

183

H

2

CO

3

⇄ 2 H

+

+ CO

3

2−

. According to the law of chemical equilibrium for the case where a product (here the hydrogen-ion) appears twice on one side of the reaction equation, we have, for the condition of equilibrium (p.

94

)

[H⁺]² × [CO₃²⁻] / [H₂CO₃] = K.

(1)

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

[H⁺] × [HCO₃⁻] / [H₂CO₃] = K₁.

(2)

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

[H⁺] × [CO₃²⁻] / [HCO₃⁻] = K₂.

(3)

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⁻])

(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 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

BaSO₄ ⇄ Ba²⁺ + SO₄²⁻ and Ba²⁺ + SO₄²⁻ + H⁺ + HSO₄⁻ ⇄ Ba²⁺ + 2 HSO₄⁻.

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:

Ba²⁺ + 2 HSO₄⁻ → Ba²⁺ + 2 H⁺ + 2 SO₄²⁻ → BaSO₄ ↓ + 2 H⁺ + SO₄²⁻.

[p104]

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

[p105]

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 of Bases.

—The same relations hold for bases as for acids: the weaker bases give ionization constants as

[p106]

do the weaker acids; the strong bases, again, as was mentioned above, do not give constants. The values for strong bases, stated in the following table, are bracketed, and refer to the ionization in 0.1 molar solutions of the bases. Polyvalent bases, like polybasic acids, ionize in stages, and the primary ionization is usually stronger than the secondary ionization, and so forth. For instance, a study of ferric chloride solution shows that the third hydroxide group of ferric hydroxide, Fe(OH)

3

, must have the smallest ionization constant.

193

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

While the constants of a large number of organic bases194 have been determined few constants of inorganic bases are as yet known. The fact that the majority of inorganic bases are polyvalent and difficultly soluble has made their examination in this respect more difficult. From the study of the decomposition of salts by water (see Chapter X), the trivalent bases, such as [p107] ferric hydroxide and aluminium hydroxide, are found to be much weaker than bivalent bases like cadmium, zinc and lead hydroxides,195 but the data are not sufficient for the calculation of any constants, or for distinguishing between the ionization of the first, second and third hydroxide groups.

The difference in ionization and in chemical activity between a strong base, like sodium or potassium hydroxide, and a weak base, like ammonium hydroxide, has already been discussed and illustrated (see p. 77). In analysis, advantage is frequently taken of these relations.196

The Ionization of Salts.

—While we read and hear a good deal about strong and weak acids, and strong and weak bases, the expression "strong" or "weak" salt is never heard; as a matter of fact, all salts, with very few exceptions, ionize exceedingly readily—about as readily as the strongest acids and bases. There are minor differences, but none of great moment—none of the kind indicated by the wide range of constants for the acids and bases. There are only a few important exceptions to this general rule—the most important ones, among the common salts, being mercuric chloride and mercuric cyanide: their exceptional behavior in regard to ionization, as indicated by their conductivities (see below), is found side by side with an exceptional chemical behavior, exactly as the theory of ionization would lead us to anticipate, and it renders necessary certain precautions, particularly in analytical work, which will be discussed later (Chap. VI). Ordinary salts are all ionized readily: for instance, whereas acetic acid in molar solution is ionized only to the extent of 0.37 per cent, its salts are highly ionized, the degree of ionization of sodium acetate, for example, being 52.8% in molar solution. As in the case of the strong acids and bases, salts of the type MeX, which ionize according to the equation MeX ⇄ Me

+

+ X

−

and which, according to the law of chemical equilibrium, might be

expected

to give a constant ratio [Me

+

][X

−

] / [MeX], do

not

give a

constant ratio

. That is, when the values obtained for the concentrations of the ions and of the nondissociated molecules, in solutions of various

[p108]

strengths, are substituted in this formula, different values are obtained.

197

For potassium chloride, we have the following relations:

Molar Concentration. Conductivity. Per cent Ionized. Ratio.

0. 131.2 100 ———

0.001 127.6 97.3 0.035

0.01 122.5 93.4 0.130

0.05 115.9 88.4 0.335

0.10 111.9 85.1 0.485

0.20 107.7 82.1 0.754

0.50 102.3 77.9 1.38

1.00 98.2 74.9 2.23

The Ionization of Strong Electrolytes and the Law of Chemical Equilibrium.

—The fact that the ionization of good electrolytes does not seem to conform to the law of chemical equilibrium is an exceedingly important one—it is, perhaps, the most important problem demanding rigorous investigation, which is before chemists at the present time. It has been used as an argument against the whole theory of ionization, and is the most important objection that has been urged against it. But, to the impartial observer, this single discrepancy, between observation and what we might have anticipated, will only prove a stronger stimulus to keener investigation and to more rigorous analysis of relations, since the latter are more complex than was at first expected. Without considering the mass of evidence in favor of the theory, found in other fields of chemistry and in physics, a part of which has been given above, we must remember that this fundamental law of chemical equilibrium has already decided unequivocally in favor of the theory in hundreds of cases of the ionization of weak acids and weak bases

198

and that these are the cases where the conditions are most simple.

199

[p109]

It would lead too far from our subject to enter into a full discussion of this important question. It will be sufficient here to indicate two directions of inquiry, which promise to lead to an explanation of the apparent contradiction between the demands of the law of chemical equilibrium and the ionization of strong electrolytes.

In the first place, the law of chemical equilibrium is based thermodynamically, i.e. from the point of view of the ultimate energy relations involved, on the assumption that none but negligible forces of attraction or repulsion exist between the molecules, whose concentrations are factors in the equilibrium equations (cf. p. 95).200 Now, in solutions of electrolytes this condition is not strictly fulfilled under any circumstances; the attractions between ions of opposite charge and the repulsions of ions of like charge, as well as the effect of charged particles on neutral molecules, come into play. For strong electrolytes, where the proportion of charged particles is always a large one, the deviations from the simpler conditions to which alone the law is really applicable must be very much greater than for weak electrolytes. It is, therefore, probable that these electrical forces201 are the source of the deviation of the ionization of strong electrolytes from the law of chemical equilibrium: although ionization is a reversible reaction, forces come into play which make the simple law inapplicable, and it is altogether likely, therefore, that we shall find, when all the factors have been investigated, that strong electrolytes should not and cannot obey this law alone.202 In confirmation of this conclusion, recent careful calculations203 have shown that entirely analogous deviations from the equilibrium law become perceptible in rather concentrated solutions of weak electrolytes, such as acetic acid, in which there is an accumulation of charged particles, more nearly akin to that present in dilute solutions of strong electrolytes. So it appears more and more certain that the deviations are a result of the presence of electrically charged components in the solutions, the amount of deviation depending on their concentration.

The "Salt Effect".

—In the second place,

204

it seems possible that the presence of strong electrolytes in a solution may modify the

ionizing power of the solvent

in such a way as to increase it, and to increase it the more, the more concentrated the ions are in the solution.

205

The ionizing power of solvents, as has been explained, is intimately connected with their dielectric properties.

[p110]

Now, solid salts have higher dielectric constants than has206 solid water, and the dielectric constant of a compound is usually much higher in the liquid than in the solid form.207 It is possible, therefore, that the presence of salts in the solution increases the dielectric or, at any rate, the ionizing power of the solvent and there are many facts which would be explained by such a behavior. Unfortunately for any decision of the question, determinations of the dielectric constants of salt solutions have given contradictory results; the more recent, and possibly more reliable results of Drude208 indicate that salt solutions show approximately the same dielectric behavior as water itself. Smale, in Nernst's laboratory, on the other hand, obtained results indicating that salt solutions have decidedly higher dielectric constants than pure water.209 A final decision in the matter would be of great importance.210 But, as explained before (p. 64), there are other properties of a solvent which seem to be intimately related to its ionizing power and which may be modified by the presence of salts, i.e. of strong electrolytes. The value obtained for the proportion [Me⁺] × [X⁻] / [MeX] grows rapidly with increasing concentration, indicating a disproportionately large ionization in the more concentrated solutions—which is what one would expect, if electrolytes or their ions in some way increased the ionizing power of the medium. In agreement with such a conclusion, Arrhenius found211 that the ionization of weak acids, like acetic acid, is increased by the presence of foreign neutral salts, such as sodium chloride. This means, of course, that the strength of acetic acid, as an acid, is increased likewise.

Exp. 0.5 c.c. of 0.1 molar acetic acid is added to 100 c.c. of a dilute solution of methyl orange in each of three test glasses. When some solid sodium chloride (3 grams, and then 3 grams more—altogether 0.1 mole) is added to the one solution, a plain increase in the intensity of the acid tint is observed.212 The addition of cane sugar to a second solution has no such effect. The addition of sodium chloride to a fourth portion of the methyl orange, to which no acetic acid has been added, shows that its color remains unchanged: the effect on the indicator in the first case, then, is the result of the action of the salt on the acetic acid.213 [p111]

The so-called "salt-effect" on the ionization of ammonium hydroxide may be illustrated in a similar way.

Exp. 0.5 cc of 0.1 molar ammonium hydroxide is added to each of two portions (100 c.c.) of a dilute solution of phenolphthaleïn. When some sodium chloride solution is then added to one of the two portions, the basicity of the solution is distinctly increased. The addition of sodium chloride to a third portion of the phenolphthaleïn solution shows that its own reaction to the indicator is neutral.

If the ionizing power of a solvent is changed by the presence of an electrolyte, then the law of chemical equilibrium, in its simple form, would not apply to the ionization of such electrolytes in varying concentrations—as little as we should expect to obtain the same constant for acetic acid in aqueous solution and in alcoholic solution, the ionizing power of alcohol being much smaller than that of water. The deviation from the law, naturally, would be most marked in the case of those electrolytes which ionize so easily as readily to produce high concentrations of ions.

It may be said that laws based on the electrical properties of salt solutions seem to be the predominating laws governing the ionization of electrolytes and modifying, in certain cases, the chemical laws based on the study of non-electrolytes.214

For the purposes of qualitative analysis, it will suffice to bear in mind the fact that the ionization215 of salts, strong acids and strong bases does not conform to the laws of mass action, and the fact that practically all salts (with the notable exceptions, among common salts, given on p. 107) are very readily ionized in aqueous solution, namely to the extent of 40 to 85% in solutions of such moderate concentration as 0.1 molar.216

Some Applications of the Law of Chemical Equilibrium.

—According to the discussions given above, for the ionization of acetic acid, CH

3

CO

2

H ⇄ CH

3

CO

2

−

+ H

+

we have the relation

[CH₃CO₂⁻] × [H⁺] / [CH₃CO₂H] = K_ionization.

[p112]

If the concentrations of the components are modified in any way, the condition of equilibrium is disturbed and change will result, always toward the restoration of equilibrium. The changes, in the case of purely ionic actions, are found to take place with an enormous velocity, equilibrium being restored almost instantly.

(1) If the solution of acetic acid, represented in the above equation, is diluted by an equal volume of water, the condition of equilibrium is disturbed:

½ [CH₃CO₂⁻] × ½ [H⁺] / (½ [CH₃CO₂H]) < K_ionization.

The ratio is smaller than that required for equilibrium, and there will be a change towards increasing the ratio. The acid will ionize more rapidly than it will be formed from the acetate and hydrogen ions (which collide less frequently in the diluted solution) and a new condition of equilibrium will be reached, when more of the acid is ionized. We found, as a matter of fact, that the more a solution of acetic acid is diluted, the larger is the proportion of ionized acid (see p. 99).

(2) If the concentration of the acetate-ion is increased in the solution by the addition of a salt of acetic acid, say sodium acetate, we have

x [CH₃CO₂⁻] × [H⁺] / [CH₃CO₂H] > K_ionization.

The ratio is larger than allowed by the equilibrium law, and the acetate ions will combine with the hydrogen ions to form acetic acid more rapidly than the ions are formed from it, until equilibrium is reëstablished. In a molar solution of acetic acid, 0.42% of the acid is ionized, and we have

[CH₃CO₂⁻] × [H⁺] / [CH₃CO₂H] = 0.0042 × 0.0042 / 0.9958 = 1.8E−5.

If an equivalent quantity of sodium acetate should be added, i.e. one mole or 82 grams of the salt per liter, the salt being ionized to the extent of 53%, we would have

0.534 × 0.0042 / 0.9958 > 1.8E−5.

The equilibrium constant will be satisfied (and the velocity of ionization of the acetic acid will become equal to the velocity of its [p113] formation from its ions) when217 [CH₃CO₂⁻] = 0.53, [H⁺] = 0.000,034 and [CH₃CO₂H] = 0.999,966. If we use two characteristic places in the decimals, we have

(0.53 × 0.000034) / 1 = 1.8E−5.

The most significant fact in the new condition of equilibrium is the extremely small concentration of hydrogen-ion in the solution. Since the acid properties of acetic acid are due to its forming hydrogen-ion, we would conclude that such properties of acetic acid are very much weakened by the presence of its own salts. This conclusion has been fully verified by careful quantitative measurements and can be demonstrated as follows218:

Exp. To two of three portions of a dilute solution of methyl orange equal quantities of acetic acid are added (e.g. 0.5 c.c. molar acid), the third portion being reserved to show the color of the neutral solution of the indicator. Now, if into one of the solutions, to which acetic acid has been added, a few crystals of sodium acetate are gradually dropped, the color reverts gradually to the color of the original neutral solution; the concentration of hydrogen-ion becomes so small, that it does not visibly affect this indicator, which is not very sensitive to acids, (H⁺).219

The solution, according to the views expressed, should still be very slightly acid, and by the use of an indicator (litmus paper) which is much more sensitive to the hydrogen-ion than is methyl orange, no difficulty is found in recognizing this fact also. As a matter of experiment, then, an acid like acetic acid is very much weaker in the presence of its own salts than in their absence, and the equilibrium constant and the concentrations of the components used determine the extent to which the hydrogen-ion is suppressed. The same must be true for all weak acids and similar relations must [p114] hold for all weak bases220—in general, weak acids and weak bases are very much weakened by the addition of their own salts.

The importance of recognizing such changes, in considering analytical reactions, may be illustrated as follows:

Exp. A solution of ferrous acetate (ferrous chloride with an equivalent quantity of sodium acetate) is treated with hydrogen sulphide; a precipitate of black ferrous sulphide is formed. A second portion of the solution is first decidedly acidified with acetic acid: hydrogen sulphide does not precipitate any ferrous sulphide. Some crystals of sodium or ammonium acetate are added to the mixture and a black precipitate of iron sulphide immediately appears around the salt as it dissolves, and on mixing the contents a heavy precipitate of the sulphide throughout the vessel is formed.

It is evident that the addition of a neutral salt, containing the same negative ion as the added acid, may completely reverse the net result of a test with hydrogen sulphide.

(3) If the concentration of the hydrogen ions in the solution of acetic acid is increased by the addition of hydrochloric, or some other strong acid, equilibrium between the acetic acid and its ions will likewise be disturbed and the new condition of equilibrium will show a suppression of the acetate-ion. Instances of such action of a strong acid in suppressing the characteristic ions of weaker acids will be discussed in detail in connection with the analytical applications of hydrogen sulphide (Chap. XI), where the action is of peculiar importance. Strong bases have a similar effect on weak bases.

(4) If one of the ions of acetic acid is suppressed by the addition of some agent, equilibrium is again destroyed and the resulting change is always in the direction of reëstablishing a condition of equilibrium on the basis of the law of equilibrium. Instances of this common case, such as the neutralization of acetic or any other acid by a base, or the driving out of a weak acid, from its salts, by a strong acid, or of a weak base by a strong base, considered from the point of view of the equilibrium law, should be worked out by the student.221 [p115]

(5) The displacement of an acid (or base) in salts by another acid (or base) is subject always to the law that equilibrium is reached, when all the equilibrium constants are satisfied in the system. Very frequently, the application of the law will lead, apparently, to the incorrect conclusion that the stronger acid (or base) will always displace, more or less completely, the weaker222—an inference, out of which grew, indeed, the characterization of acids and bases as strong and weak. Yet, when the laws of equilibrium, as the result of the peculiar values of constants, demand that, on the contrary, a strong acid or base should be displaced by a weak, or even a feeble one, we find that the change in this direction occurs with equal ease. Numerous instances will be given where a weak acid (or a weak base) does this to a certain extent (Chap. X), and others where precipitation of salts facilitates the action of weaker acids greatly by the introduction of new, physical constants. The following case of the liberation of hydrochloric acid by the exceedingly weak acid, hydrocyanic acid, is important because it shows a reversal of the common action without the formation of any precipitate, and especially because it brings out most strikingly the relations between ionization and chemical activity in a case of special importance to analytical chemists.

The Exceptional Ionization of Mercuric Cyanide and Its Consequences.

—We have found that practically all salts are very readily ionized. But it was mentioned that there are a few exceptions to this rule, and mercuric chloride and especially mercuric cyanide were named as the most important exceptions from the point of view of analytical chemistry. The difference in ionization between these two salts and ordinary salts may be shown readily by the apparatus previously used to demonstrate the difference in the ionization of various bases and acids.

Exp. Into the parallel tubes of the conductivity apparatus (p. 77) equivalent quantities223 of solutions of mercuric cyanide224 Hg(CN)₂, mercuric chloride [p116] HgCl₂, and barium chloride BaCl₂, are introduced. The barium chloride represents an ordinary salt of the same type as the mercury salts, and the current passing through its solution makes the little lamp glow. The electrodes in the mercuric chloride solution must be brought quite close together before sufficient current will pass through the solution to bring its little lamp to redness. In the case of the cyanide we can, at most, get a faint, dull glow by bringing the electrodes together as closely as we can, without allowing them to touch each other and short-circuit the current.

It is evident that these mercury salts are not as readily ionizable as are ordinary salts. This difference, as may be anticipated, shows itself also in the chemical behavior of their solutions and makes necessary special precautions on the part of the analyst in examining mercury compounds. For instance, whereas mercuric oxide is readily precipitated by the addition of sodium hydroxide to solutions of the nitrate and even of the moderately ionized chloride, one fails to get a precipitate of oxide from the cyanide solution (exp.), and if we relied on this test, we should overlook the mercury entirely. That traces of the mercuric-ion are present, as indicated by the minimal conductivity of the cyanide, is confirmed by the fact that from the cyanide solution the sulphide, which is much less soluble than is the oxide, may be precipitated by the addition of ammonium sulphide (exp.). That the sulphide is in fact less soluble225 than the oxide is shown by the conversion of the latter into the former by the action of ammonium sulphide (exp.).

As a further result of the abnormally slight ionization of these mercury salts, the analyst, unless he is on his guard, may also have difficulty in discovering the presence of their negative ions. Thus, while sodium chloride readily gives hydrogen chloride when treated with concentrated sulphuric acid, mercuric chloride, although it is a soluble salt, does not (exp.), and reliance on this test alone might lead to a gross error.226 In the case of the cyanide, it is correspondingly difficult to recognize the [p117] cyanide-ion (see the laboratory experiment, Part III). The ordinary tests fail to show its presence until the mercury has been removed from the solution by precipitation as a sulphide. Mercuric cyanide being a deadly poison which analysts are liable to meet and have met with in criminal cases, it is clear that a knowledge of these facts is vital to analytical accuracy.

Now, the very slight ionization of mercuric cyanide enables us to realize, in the following experiment, the case where an exceedingly weak acid without the formation of any precipitate involving physical constants, may displace a much stronger acid from its salts. Hydrocyanic acid is one of the weakest acids (table, p. 104), the constant for the ratio [H⁺] × [CN⁻] / [HNC] being 0.7E−9. It is so weak an acid that the addition of a dilute solution to methyl orange will not redden the indicator, but will have only a barely perceptible effect on it (exp.). Mercuric chloride solutions also are almost neutral to methyl orange (exp.) (very slight decomposition of the salt by water makes the solution very slightly acid, not enough to produce more than an orange color with methyl orange). Now, mercuric chloride, while it is not very easily ionized, is, we found, very much more readily ionized than is mercuric cyanide. The consequence is that when we add hydrocyanic acid to a mercuric chloride solution, the equilibrium between mercuric chloride and its ions and between hydrocyanic acid and its ions will be decidedly displaced, the mercuric-ion combining with the cyanide-ion to form the scarcely ionizable mercuric cyanide. As a result, more and more of the molecular mercuric chloride and hydrocyanic acid will be ionized; and since the other ions, the chloride and the hydrogen ions, form a readily ionizable electrolyte, hydrochloric acid, these ions (H⁺ and Cl⁻) will accumulate in the solution and we shall have sufficient ionized hydrochloric acid liberated to make the solution decidedly acid.

Exp. When the two solutions described above are mixed, a strongly acid solution, colored a bright pink, results.

In the following equations the dark arrows indicate the direction in which the action goes when the solutions are mixed:

HgCl₂ ⥂ Hg²⁺ + 2 Cl⁻ 2 HCN ⥂ 2 CN⁻ + 2 H⁺ 2 CN⁻ + Hg²⁺ ⥂ Hg(CN)₂ 2 Cl⁻ + 2 H⁺ ⇄ 2 HCl