ELECTROLYTIC SOLUTIONS
_Solutions which conduct Electricity._--The laws of solution which we have
studied in the previous chapter apply only to those solutions, chiefly of
organic origin, which do not conduct electricity. Solutions of electrolytes
such as the ordinary salts, acids, and bases, which are ionized on
solution, give values for the various constants of solution which do not
accord with those required by theory. If, for instance, we take a
gramme-molecule of an electrolyte such as chloride of sodium, and dissolve
it in a litre of water, we find that the lowering of the freezing point is
nearly double the theoretical value of 1.85deg. The same holds good for the
osmotic pressure, and for all the constants which are proportional to the
molecular concentration of the solute. The solution behaves, in each case,
as if it contained more than one gramme-molecule of sodium chloride per
litre. It behaves, in fact, as if it contained i times the number of
molecules of solute originally introduced into it. If n be the original
number of molecules, then it will apparently contain n' = in molecules.
This law is universal for all electrolytic solutions; the theoretical value
for their concentration, osmotic pressure, and all the proportional
physical constants must be multiplied by this quantity, i = n'/n, which is
the ratio of the apparent number of the molecules present to the number
originally introduced.
A similar dissociation of the molecule is observed in the case of many
gases. The vapour of chloride of ammonium, for instance, is decomposed by
heat, and it may be shown experimentally that the increase of pressure on
heating above {25} that which theory demands, is due to an increase in the
number of the gaseous molecules present. Some of the vapour particles are
dissociated into two or more fragments, each of which plays the part of a
single molecule.
Arrhenius, in 1885, advanced the hypothesis that the apparent increase in
the number of molecules of an electrolytic solution was also due to
dissociation. This interpretation at once threw a flood of light on a
number of phenomena hitherto obscure.
_Coefficient of Dissociation._--We have seen that in order to obtain values
which accord with experiment we have to multiply the number of
gramme-molecules of the solute by the coefficient i, which is called the
Coefficient of Dissociation.
This coefficient of dissociation, i, may be found by observing the lowering
of the freezing point of a normal solution, and dividing it by 1.85. i =
t/1.85.
The coefficient of dissociation varies with the degree of concentration of
the solution, rising to a maximum when the solution is sufficiently
diluted.
If we know i, the coefficient of dissociation for a given solute, contained
in a solution of a definite concentration, we can find n', the number of
particles present in a solution containing n gramme-molecules of the solute
per litre, since n' = in. On the other hand, if from a consideration of its
freezing point and other constants we find that an electrolytic solution
appears to contain n' gramme-molecules per litre, the real number of
chemical gramme-molecules in one litre of the solution will be only n' / i
= n.
Very concentrated solutions do not conform to these laws. In this they
resemble gases, which as they approach their point of condensation tend
less and less to conform to the laws of gaseous pressure.
_Electrolysis._--If we take a solution of an acid, a salt, or a base, and
dip into it two metallic rods, one connected to the positive and the other
to the negative pole of a battery, we {26} find that the metals or metallic
radicals of the solution are liberated at the negative pole, while the acid
radicals of the salts and acids and the hydroxyl of the bases are liberated
at the positive pole. The liberated substances may either be discharged
unchanged, or they may enter into new combinations, causing a series of
secondary reactions.
_Electrolytes._--Solutions which conduct electricity are called
Electrolytes, and the conducting metallic rods dipping into the solution
are the Electrodes. Faraday gave the names of Ions to the atoms or
atom-groups liberated at either electrode. The ions liberated at the
positive electrode are the Anions, and those at the negative electrode are
the Cations. The only solutions which possess any notable degree of
electrical conductivity are the aqueous solutions of the various salts,
acids, and bases, and in these solutions only do we meet with those
phenomena of dissociation which are evidenced by anomalies of osmotic
pressure, freezing point and the like,--anomalies which show that the
solution contains a greater number of molecules than that indicated by its
molecular concentration. These anomalies are due to dissociation, the
division of some of the molecules into fragments, each of which plays the
part of a separate molecule, contributing its quota to the osmotic tension
and vapour pressure of the solution, in fact to all the phenomena which are
dependent on the degree of molecular concentration. The electrical
conductivity of a solution is therefore proved to be dependent on its
molecular dissociation.
_Arrhenius' Theory of Electrolysis._--In 1885, Arrhenius brought forward
his theory of the transport of electricity by an electrolyte. According to
this hypothesis, the electric current is carried by the ions, the positive
charges by the cations, and the negative charges by the anions. In virtue
of the attraction between charges of different sign, and repulsion between
charges of like sign, the cations are repelled by the positive charge on
the anode, and attracted by the negative charge on the cathode. Similarly
the anions are repelled by the cathode and attracted by the anode. {27}
An electrolytic solution contains three varieties of particles, positive
ions or cations, negative ions or anions, and undissociated neutral
molecules. The molecular concentration of such a solution, with the
corresponding constants, depends on the total number of these particles,
_i.e._ the sum of the ions and the undissociated neutral molecules. We may
indicate an ion by placing above it the sign of its electrical charge, one
sign for each valency. Thus Na^+ and Cl^- indicate the two ions of a salt
solution; Cu^{++} and SO_4^{--} the two ions of a solution of sulphate of
copper. A point is sometimes substituted for the + sign, and a comma for
the - sign. Thus Na^. and Cl^,; Cu^{..} and SO_4^{,,}.
My friend Dr. Lewis Jones has given a very vivid picture of the processes
which go on in an electrolytic solution when an electric current is
passing. He compares an electrolytic cell to a ballroom, in which are
gyrating a number of dancing couples, representing the neutral molecules,
and a number of isolated ladies and gentlemen representing the anions and
cations respectively. If we suppose a mirror at one end of the ballroom and
a buffet at the other, the ladies will gradually accumulate around the
mirror, and the gentlemen around the buffet. Moreover, the dancing couples
will gradually be dissociated in order to follow this movement.
_Degree of Dissociation._--The degree of dissociation is the fraction of
the molecules in the solution which have undergone dissociation. Let n be
the total number of molecules of the solute, and n" the number of
dissociated molecules. Then n" / n = a will represent the degree of
dissociation. Let k be the number of ions into which each molecule is
split. Then a = n"k / nk, _i.e._ the degree of dissociation is the ratio of
the number of ions actually present in a solution to the number which would
be present if all the molecules of the solute were dissociated.
Let n' be the total number of particles present in a solution {28}
containing n molecules, each of which is composed of k ions. Then if a is
the degree of dissociation,
n' = n - an + ank,
n' = n[1 + a (k - 1)],
n' / n = 1 + a (k - 1) = i.
We thus obtain i the coefficient of dissociation, in terms of the degree of
dissociation a and the number of ions in each molecule k.
If there is no dissociation, _i.e._ if a = 0, then n' = n, and i = 1. If
all the molecules are dissociated, a = 1, and i = k.
_Faraday's Law._--Faraday found that the quantity of electricity required
to liberate one gramme-molecule of any radical is 96.537 coulombs for each
valency of the radical.
_Electrochemical Equivalent._--The electrochemical equivalent of a radical
is the weight liberated by one coulomb of electricity. It is equal to the
molecular weight of the ion, divided by 96.537 times its valency.
_Electrolytic Conductivity._--The conductivity of an electrolyte is the
inverse of its resistance. C = 1/R.
For a given difference of potential the conductivity of an electrolyte is
proportional to the number of ions in unit volume, the electrical charge on
each ion, and the velocity of the ions.
_The specific conductivity_ [Delta] of an electrolyte is the conductivity
of a cube of the solution, each face of which is one square centimetre in
area. The _molecular conductivity_ of an electrolyte is the conductivity of
a solution containing one gramme-molecule of the substance placed between
two parallel conducting plates, one centimetre apart. The molecular
conductivity is independent of the volume occupied by the gramme-molecule
of the solute, depending only on the degree of dissociation. The molecular
conductivity U is equal to the product of V, the volume of the molecule, by
[Delta], its specific conductivity. U = V[Delta]. Whence [Delta] = U / V,
_i.e._ the specific {29} conductivity equals the molecular conductivity
divided by the volume.
The conductivity of an electrolyte is proportional to the number of ions in
a volume of the solution containing one gramme-molecule. Let M_{[infinity]}
be the conductivity for complete dissociation and M_v the molecular
conductivity at the volume V. Then
M_v / M_{[infinity]} = n"k / nk = n" / n = a,
the degree of dissociation. This is Ostwald's law, which says that the
degree of dissociation is equal to the ratio of conductivity when the
gramme-molecule occupies a volume V, to its conductivity when the solution
is so dilute that dissociation is complete. Hence the degree of
dissociation may also be determined by comparing the electrical
conductivities of two solutions of different degrees of concentration.
| -- -- -- | -- -- -- |
| SO_4 SO_4 SO_4 | SO_4 SO_4 SO_4 |
| | |
| ++ ++ ++ | ++ ++ ++ |
| Cu Cu Cu | Cu Cu Cu |
| | |
+----------------------------+--------------------------------+
FIG. 1.--Before the passage of the current.
| -- | -- -- |
| SO_4 | SO_4 SO_4 SO_4 SO_4 SO_4 |
- | | | +
| ++ | ++ ++ |
| Cu Cu Cu Cu | Cu Cu |
| | |
+---------------------------+---------------------------------+
FIG. 2.--After the passage of the current.
_Velocity of the Ions._--If the electrolytic cell is divided into two
segments by means of a porous diaphragm, we shall find after a time an
unequal distribution of the solute on the two sides. For instance, with a
solution of sulphate of copper, after the current has passed for some time
there will be a diminution of concentration in the liquid on both sides of
the diaphragm, but the loss will be very unequally divided. Two-thirds of
the loss of concentration will be on the side of the negative electrode and
only one-third on the positive side. In 1853, Hittorf gave the following
ingenious explanation of this phenomenon:-- {30}
Fig. 1 represents an electrolytic vessel containing a solution of sulphate
of copper, the vertical line indicating a porous partition separating the
vessel into two parts. Fig. 2 shows the same vessel after the passage of
the current. The acid radical has travelled twice as fast as the metal. For
each copper ion which has passed through the porous plate towards the
cathode two acid radicals have passed through it towards the anode. Three
ions have been liberated at either electrode, but in consequence of the
difference of velocity with which the positive and the negative ions have
travelled, the negative side of the vessel contains only one molecule of
copper sulphate and has lost two-thirds of its molecular concentration,
while the positive side contains two molecules of copper sulphate and has
only lost one-third of its concentration. This proves clearly that the ions
move in different directions with different velocities. Let u be the
velocity of the anions, and v the velocity of the cations. Let n be the
loss of concentration at the cathode, and 1 - n the loss of concentration
at the anode. Then
u / v = n / (1 - n),
_i.e._ the loss of concentration at the cathode is to the loss of
concentration at the anode as the velocity of the anions is to that of the
cations. Hence by measuring the loss of concentration at the two
electrodes, we have an easy means of determining the comparative velocity
of different ions.
In 1876, Kohlrausch compared the conductivity of the chlorides, bromides,
and iodides of potassium, sodium, and ammonium respectively. He found that
altering the cation did not affect the _differences_ of conductivity
between the three salts, thus showing that these differences of
conductivity were dependent on the nature of the anion only, and not on the
particular base with which it was combined. The difference of conductivity
between an iodide and a bromide, for example, is the same whether
potassium, sodium, or ammonium salts are compared. A similar experiment has
been made with a series of cations combined with various anions. The
difference of conductivity of the salts in the series is the same whichever
anion is used, _i.e._ the difference of conductivity between potassium
chloride and sodium chloride is the same as that between {31} potassium
bromide and sodium bromide. Hence we may conclude that the conductivity of
any salt is an ionic property.
Kohlrausch's law may be expressed by the formula c = d(u + v), where c is
the conductivity of the salt, d the degree of dissociation, _i.e._ the
fraction of the electrolyte broken up into ions, and u and v the velocity
of the anions and cations respectively. When all the molecules of the
electrolyte are dissociated, d = 1, and the formula becomes c_{[infinity]}
= u + v.
As we have already seen, a salt is formed by the union of a metal M with an
acid radical R. Potassium sulphate, K_2SO_4, consists of the metal K_2 and
the acid radical SO_4. Ammonium chloride, NH_4Cl, consists of the basic
radical NH_4 and the acid radical Cl. The various acids may be considered
as salts of the metal hydrogen. Thus sulphuric acid, H_2SO_4, is the
sulphate of hydrogen. Bases may be considered as salts with the hydroxyl
group, OH, replacing the acid radical. Thus potash, KOH, is the hydroxyl of
potassium. The various electrolytic combinations may be represented by the
following symbols:--
Salts = MR.
Acids = HR.
Bases = MOH.
The various chemical reactions of an electrolyte are all ionic reactions,
the chemical activity of an electrolytic solution being proportional to its
electric conductivity, _i.e._ the degree of dissociation of its ions. The
acidity of an electrolytic solution is due to the presence of the
dissociated ion H^+, and its strength is determined by the concentration of
these free hydrogen ions. Hence the greater the degree of dissociation the
stronger the acid.
The basic character of a solution is determined by the presence of the
hydroxyl radical OH^-. The greater the concentration of the hydroxyl ions,
_i.e._ the greater the dissociation, the stronger is the base.
The ions H^+ and OH^- are of special importance, since they are the ions of
water, H_2O = H^+ + OH^-. The degree of {32} dissociation of pure water is
but small. Water is, however, the most important of all the various agents
in the chemical reactions of life, since a large number of organic
substances are decomposed by water by a process of hydrolysis, and a vast
number of organic substances are but combinations of carbon with the ions
H^+ and OH^-, their diversity being due to variations in the relative
proportions and grouping.
_The Chemical, Therapeutic, and Toxic Actions of Ions._--The chemical,
therapeutic, antiseptic, and toxic actions of electrolytic solutions are
almost exclusively due to ionization. Take, for instance, a solution of
nitrate of silver in which the addition of chlorine produces a white
precipitate of chloride of silver. This precipitate occurs only when the
solution added is one such as NaCl, where the chlorine is present as the
free ion Cl^-. No such precipitate is produced in a solution of chlorate of
potassium or chloracetic acid, where the chlorine is entangled in the
complex ion ClO_3 or C_2H_3ClO_2.
Since, then, the toxic and pharmacological properties of an electrolyte
depend entirely on the ionic grouping, it behoves the physician and the
biologist to study the structure and grouping of the ions in a molecule,
rather than that of the atoms. Consider for a moment the totally different
properties of the phosphides and the phosphates. The former are extremely
toxic, while the latter are perfectly harmless. There is not the slightest
analogy between their actions on the living organism. On the other hand,
all the phosphides produce the same toxic and therapeutic effects, whatever
the cation with which they are united. Their toxic properties are derived
from the presence of the free phosphorus ion P^{---}. The phosphates
contain phosphorus in the same proportion as the phosphides, but this
phosphorus is harmlessly entangled in the complex ion PO_4^{---}, whose
properties are absolutely different from those of the ion P^{---}.
The above considerations apply equally to the chlorides and chlorates, the
iodides and iodates, the sulphides and sulphates, and in general to all
chemical salts. {33}
The question has an intimate bearing on practical pharmacology. When we
prescribe a cacodylate or an amylarsinate, we are not prescribing an
arsenical treatment whose effects can be compared with those of an
arsenide, an arsenite, or an arsenate. This fact is sufficiently indicated
by the difference in the toxic doses of the different salts. Each variety
of arsenical ion has its own special physiological and therapeutic
properties. We do not expect to obtain the results of a ferruginous
treatment from the administration of a ferrocyanide or a ferricyanide. Both
contain iron, it is true, but neither possess the properties of the cation
Fe^{+++}, but rather those of the complex anion of which they form a part.
We have already said that most of the therapeutic, toxic, and caustic
actions of an electrolyte are due to ionic action, and the substances can
therefore have no toxic action unless they are dissociated. Many of the
solvents employed in medicine, such as alcohol, glycerine, vaseline, and
chloroform dissolve the electrolytes but do not dissociate them into ions,
and these solutions therefore do not conduct electricity. Such solutions
have no therapeutic action. With the absence of dissociation all the ionic
toxic and caustic effects also disappear entirely, and only re-appear as
the water of the tissue is able slowly to effect the necessary
dissociation.
Carbolic acid dissolved in glycerine is hardly caustic and but very
slightly toxic. We have met with several instances in which a tablespoonful
of carbolized glycerine, in equal parts, has been swallowed without any ill
effect, either caustic or toxic, whereas the same dose dissolved in water
would have been fatal. This absence of dissociation has enabled the surgeon
Menciere to inject carbolic and glycerine in equal proportions into the
larger joints, the part being subsequently washed out with pure alcohol.
Thus by employing vaseline, oil, or glycerine as a solvent, and avoiding
the access of water, we are able to use electrolytic antiseptics in very
concentrated form. Their action is brought out very slowly, as the water of
the organism effects the necessary dissociation of the electrolyte. {34}
Since all chemical, toxic, and therapeutic actions are ionic, they are
proportional to the degree of ionic concentration, _i.e._ to the number of
ions in a given volume. The only point of importance, that which determines
their activity, whether chemical or therapeutic, is the degree of
ionization or dissociation. For example, all acids have the same cation
H^+. They have all identical properties, but they differ widely in the
intensity of their action. There are weak acids such as acetic acid, and
strong acids like sulphuric acid. The stronger acids are those which are
more thoroughly dissociated, and in which the ion H^+ is very concentrated;
whereas the feeble acids are but slightly dissociated, so that the ion H^+
is less concentrated.
Paul and Kroenig have shown that the bactericidal action of different salts
also varies with their degree of dissociation, _i.e._ with the
concentration of the active ions. They made a series of observations on the
bactericidal action of various salts of mercury, the bichloride, the
bibromide, and the bicyanide, on the spores of _Bacillus anthracis_. The
following results were obtained from a comparison of solutions containing 1
gramme-molecule of the salt in 64 litres of water. With the bichloride
solution, after exposure to the solution for twenty minutes, only 7
colonies of the bacillus were developed. After exposure to a similar
solution of the bibromide the number of colonies was 34. The antiseptic
action of the bichloride was therefore five times as great as that of the
bibromide. The bicyanide of mercury, however, even when four times as
concentrated, permitted the growth of an enormous number of colonies,
showing that it had no appreciable antiseptic action whatever.
Nevertheless, the proportion of Hg is the same in all the solutions, and if
there were any difference one would naturally expect that the ion Cy^-
would be more toxic than Cl^- or Br^-. The real condition which varies in
these solutions and determines their activity is the degree of
dissociation. The whole of the antiseptic property resides in the ion
Hg^{++}. This ion is very {35} concentrated in the highly dissociated
solution HgCl_2, less concentrated in the less ionized solution HgBr_2, and
exceedingly dilute in the HgCy_2, which is hardly ionized at all.
What is true of the bactericidal action of the salts of mercury is equally
true of their therapeutic effect. It is a great mistake to estimate the
medicinal activity of a solution of a salt of mercury, or indeed of any
electrolytic solution, simply by its degree of molecular concentration. The
important point is the degree of dissociation, which is the only true
measure of its activity. In the intramuscular injection of mercury salts it
is by no means a matter of indifference what salt we employ. A salt should
be used such as the bichloride or the biniodide, which is easily
dissociated. Other salts are often employed because they occasion less pain
at the site of injection; but the pain is a sign of the degree of activity
of the preparation. The pain, it is true, may be avoided by using a salt
which is less easily dissociated, or in which the mercury is bound up in a
complex ion, but by so doing we diminish the efficacy of the remedy. It is
moreover quite easy to diminish, or even entirely to suppress, the pain, by
using a very dilute solution of an active ionized salt. A one-half per
cent. or even one-quarter per cent. solution of the bichloride or biniodide
of mercury may be injected very slowly in sufficient quantity without
producing the slightest discomfort. Local action depends entirely on ionic
concentration. One drop of pure sulphuric acid will destroy the skin,
whereas the same amount if diluted in a tumblerful of water will furnish a
refreshing drink.
* * * * *
{36}