Chapter XXII: ) acidulated with acetic acid gives a salt which after (2)

_Manganous chloride_, MCl_{2}, crystallises with 4 mol. H_{2}O,
like the ferrous salt, and not with 6 mol. H_{2}O like many
kindred salts--for example, those of cobalt, calcium, and
magnesium; 100 parts of water dissolve 38 parts of the anhydrous
salt at 10° and 55 parts at 62°. Alcohol also dissolves manganous
chloride, and the alcoholic solution burns with a red flame. This
salt, like magnesium chloride, readily forms double salts. A
solution of borax gives a dirty rose-coloured precipitate having
the composition MnH_{4}(BO_{3})_{2}H_{2}O, which is used as a
drier in paint-making. Potassium cyanide produces a yellowish-grey
precipitate, MnC_{2}N_{2}, with manganous salts, soluble in an
excess of the reagent, a double salt, K_{4}MnC_{6}N_{6},
corresponding with potassium ferrocyanide, being formed. On
evaporation of this solution, a portion of the manganese is
oxidised and precipitated, whilst a salt corresponding to Gmelin's
red salt, K_{3},MnC_{6}N_{6} (_see_ Chapter XXII.), remains in
solution. Sulphuretted hydrogen does not precipitate salts of
manganese, not even the acetate, but ammonium sulphide gives a
flesh-coloured precipitate, MnS; at 320° this sulphide of
manganese passes into a green variety (Antony). Oxalic acid in
strong solutions of manganous salts gives a white precipitate of
the oxalate, MnC_{2}O_{4}. This precipitate is insoluble in water,
and is used for the preparation of manganous oxide itself because
it decomposes like oxalic acid when ignited (in a tube without
access of air), with the formation of carbonic anhydride, carbonic
oxide, and manganous oxide. _Manganous oxide_ thus obtained is a
green powder, which however oxidises with such facility that it
burns in air when brought into contact with an incandescent
substance, and passes into the red intermediate oxide Mn_{3}O_{4}.
In solutions of manganous salts, alkalis produce a precipitate of
the hydroxide MnH_{2}O_{2}, which rapidly absorbs oxygen in the
presence of air and gives the brown intermediate oxide, or, more
correctly speaking, its hydrate.

Manganous oxide, besides being obtained by the above-described
method from manganous oxalate, may also be obtained by igniting
the higher oxides in a stream of hydrogen, and also from manganese
carbonate. The manganous oxide ignited in the presence of hydrogen
acquires a great density, and is no longer so easily oxidised. It
may also be obtained in a crystalline form, if during the ignition
of the carbonate or higher oxide a trace of dry hydrochloric acid
gas be passed into the current of hydrogen. It is thus obtained in
the form of transparent emerald green crystals of the regular
system, and in this state is easily soluble in acids.

Manganous oxide in oxidising gives the _red oxide of manganese_,
Mn_{5}O_{4}. This is the most stable of all the oxides of
manganese; it is not only stable at the ordinary but also at a
high temperature--that is, it does not absorb or disengage oxygen
spontaneously. When ignited, all the higher oxides of manganese
pass into it by losing oxygen, and manganous oxide by absorbing
oxygen. This oxide does not give any distinct salts, but it
dissolves in sulphuric acid, forming a dark red solution, which
contains both manganous and manganic (of the _oxide_, Mn_{2}O_{3})
sulphates. The latter with potassium sulphate gives a manganese
alum, in which the alumina is replaced by its isomorphous oxide of
manganese. But this alum, like the solution of the intermediate
oxide in sulphuric acid, evolves oxygen and leaves a manganous
salt when slightly heated.

_Manganese dioxide_ is still less basic than the oxide, and
disengages oxygen or a halogen in the presence of acids, forming
manganous salts, like the oxide. However, if it be suspended in
ether, and hydrochloric acid gas passed into the mixture, which is
kept cool, the ether acquires a green colour, owing to the
formation of tetrachloride of manganese, MnCl_{4}, corresponding
with the dioxide which passes into solution. It is however very
unstable, being exceedingly easily decomposed with the evolution
of chlorine. The corresponding fluoride, MnF_{4}, obtained by
Nicklés is much more stable. At all events, manganese dioxide does
not exhibit any well-defined basic character, but has rather an
acid character, which is particularly shown in the compounds
MnF_{4} and MnCl_{4} just mentioned, and in the property of
manganese dioxide of combining with alkalis. If the higher grades
of oxidation of manganese be deoxidised in the presence of
alkalis, they frequently give the dioxide combined with the
alkali--for example, in the presence of potash a compound is
formed which contains K_{2}O,5MnO_{2}, which shows the weak acid
character of this oxide. When ignited in the presence of sodium
compounds manganese dioxide frequently forms Na_{2}O,8MnO_{2} and
Na_{2}O,12MnO_{2}, and lime when heated with MnO_{2} gives from
CaO,3MnO_{2} to (CaO)_{2},MnO_{2} (Rousseau) according to the
temperature. Besides which, perhaps, MnO_{2} is a saline compound,
containing MnOMnO_{3} or (MnO)_{3}Mn_{2}O_{7}, and there are
reactions which support such a view (Spring, Richards, Traube, and
others); for instance it is known that manganous chloride and
potassium permanganate give the dioxide in the presence of
alkalis.

Manganese dioxide may be obtained from manganous salts by the
action of oxidising agents. If manganous hydroxide or carbonate be
shaken up in water through which chlorine is passed, the
hypochlorite of the metal is not formed, as is the case with
certain other oxides, but manganese dioxide is precipitated:
2MnO_{2}H_{2} + Cl_{2} = MnCl_{2} + MnO_{2},H_{2}O + H_{2}O. Owing
to this fact, hypochlorites in the presence of alkalis and acetic
acid when added to a solution of manganous salts give hydrated
manganese dioxide, as was mentioned above. Manganous nitrate also
leaves manganese dioxide when heated to 200°. It is also obtained
from manganous and manganic salts of the alkalis, when they are
decomposed in the presence of a small amount of acid; the
practical method of converting the salts MnX_{2} into the higher
grades of oxidation is given in Chapter II., Note 6.

As the salts of manganous oxide MnX_{2} closely resemble (and are isomorphous with) the salts of magnesia MgX_{2} in many respects (with the exception of the fact that MnX_{2} are rose coloured and are easily oxidised in the presence of alkalis), we will not dwell upon them, but limit ourselves to illustrating the chemical character of manganese by describing the metal and its corresponding acids. The fact alone that the oxides of manganese are not reduced to the metal when ignited in hydrogen (whilst the oxides of iron give metallic iron under these circumstances), but only to manganous oxide, MnO, shows that manganese has a considerable affinity for oxygen--that is, it is difficult to reduce. This may be effected, however, by means of charcoal or sodium at a very high temperature. A mixture of one of the oxides of manganese with charcoal or organic matter gives fused _metallic manganese_ under the powerful heat developed by coke with an artificial draught. The metal was obtained for the first time in this manner by Gahn, after Pott, and more especially Scheele, had in the last century shown the difference between the compounds of iron and manganese (they were previously regarded as being the same). Manganese is prepared by mixing one of its oxides in a finely-divided state with oil and soot; the resultant mass is then first ignited in order to decompose the organic matter, and afterwards strongly heated in a charcoal crucible. The manganese thus obtained, however, contains, as a rule, a considerable amount of silicon and other impurities. Its specific gravity varies between 7·2 and 8·0. It has a light grey colour, a feebly metallic lustre, and although it is very hard it can be scratched by a file. It rapidly oxidises in air, being converted into a black oxide; water acts on it with the evolution of hydrogen--this decomposition proceeds very rapidly with boiling water, and if the metal contain carbon.[20]

[20] Other chemists have obtained manganese by different methods, and
attributed different properties to it. This difference probably
depends on the presence of carbon in different proportions.
Deville obtained manganese by subjecting the pure dioxide, mixed
with pure charcoal (from burnt sugar), to a strong heat in a lime
crucible until the resultant metal fused. The metal obtained had a
rose tint, like bismuth, and like it was very brittle, although
exceedingly hard. It decomposed water at the ordinary temperature.
Brunner obtained manganese having a specific gravity of about 7·2,
which decomposed water very feebly at the ordinary temperature,
did not oxidise in air, and was capable of taking a bright polish,
like steel; it had the grey colour of cast iron, was very brittle,
and hard enough to scratch steel and glass, like a diamond.
Brunner's method was as follows: He decomposed the manganese
fluoride (obtained as a soluble compound by the action of
hydrofluoric acid on manganese carbonate) with sodium, by mixing
these substances together in a crucible and covering the mixture
with a layer of salt and fluor spar; after which the crucible was
first gradually heated until the reaction began, and then strongly
heated in order to fuse the metal separated. Glatzel (1889)
obtained 25 grms. of manganese, having a grey colour and sp. gr.
7·39, by heating a mixture of 100 grms. of MnCl_{2} with 200 grms.
KCl and 15 grms. Mg to a bright white heat. Moissan and others, by
heating the oxides of manganese with carbon in the electric
furnace, obtained carbides of manganese--for example, Mn_{3}C--and
remarked that the metal volatilised in the heat of the voltaic
arc. Metallic manganese is, however, not prepared on a large
scale, but only its alloys with carbon (they readily and rapidly
oxidise) and _ferro-manganese_ or a coarsely crystalline alloy of
iron, manganese and carbon, which is smelted in blast-furnaces
like pig-iron (_see_ Chapter XXII.) This ferro-manganese is
employed in the manufacture of steel by Bessemer's and other
processes (see Chapter XXII.) and for the manufacture of manganese
bronze. However, in America, Green and Wahl (1895) obtained almost
pure metallic manganese on a large scale. They first treat the ore
of MnO_{2} with 30 p.c. sulphuric acid (which extracts all the
oxides of iron present in the ore), and then heat it in a reducing
flame to convert it into MnO, which they mix with a powder of Al,
lime and CaF_{2} (as a flux), and heat the mixture in a crucible
lined with magnesia; a reaction immediately takes place at a
certain temperature, and a metal of specific gravity 7·3 is
obtained, which only contains a small trace of iron.

Manganese gives two compounds with _nitrogen_, Mn_{5}N_{2} and
Mn_{3}N_{2}. They were obtained by Prelinger (1894) from the
amalgam of manganese Mn_{2}Hg_{5} (obtained on a mercury anode by
the action of an electric current upon a solution of MnCl_{2});
the mercury may be removed from this amalgam by heating it in an
atmosphere of hydrogen, and then metallic manganese is obtained as
a grey porous mass of specific gravity 7·42. If this amalgam be
heated in dry nitrogen it gives Mn_{5}N_{2} (grey powder, sp. gr.
6·58), but if heated in an atmosphere of NH_{3} it gives (as also
does Mn_{5}N_{2}) Mn_{3}N_{2}, (a dark mass with a metallic
lustre, sp. gr. 6·21), which, when heated in nitrogen is converted
into Mn_{5}N_{2}, and if heated in hydrogen evolves NH_{3} and
disengages hydrogen from a solution of NH_{4}Cl. At all events,
manganese is a metal which decomposes water more easily than iron,
nickel, and cobalt.

It has been shown above that if manganese dioxide, or any lower oxide of manganese, be heated with an alkali in the presence of air, the mixture absorbs oxygen,[21] and forms an alkaline manganate of a green colour: 2KHO + MnO_{2} + O = K_{2}MnO_{4} + H_{2}O. Steam is disengaged during the ignition of the mixture, and if this does not take place there is no absorption of oxygen. The oxidation proceeds much more rapidly if, before igniting in air, potassium chlorate or nitre be added to the mixture, and this is the method of preparing _potassium manganate_, K_{2}MnO_{4}. The resultant mass dissolved in a small quantity of water gives a dark green solution, which, when evaporated under the receiver of an air-pump over sulphuric acid, deposits green crystals of exactly the same form as potassium sulphate--namely, six-sided prisms and pyramids. The composition of the product is not changed by being redissolved, if perfectly pure water free from air and carbonic acid be taken. But in the presence of even very feeble acids the solution of this salt changes its colour and becomes red, and deposits manganese dioxide. The same decomposition takes place when the salt is heated with water, but when diluted with a large quantity of unboiled water manganese dioxide does not separate, although the solution turns red. This change of colour depends on the fact that potassium manganate, K_{2}MnO_{4}, whose solution is green, is transformed into potassium permanganate, KMnO_{4}, whose solution is of a red colour. The reaction proceeding under the influence of acids and a large quantity of water is expressed in the following manner: 3K_{2}MnO_{4} + 2H_{2}O = 2KMnO_{4} + MnO_{2} + 4KHO. If there is a large proportion of acid and the decomposition is aided by heat, the manganese dioxide and potassium permanganate are also decomposed, with formation of manganous salt. Exactly the same decomposition as takes place under the action of acids is also accomplished by magnesium sulphate, which reacts in many cases like an acid. When water holding atmospheric oxygen in solution acts on a solution of potassium manganate, the oxygen combines directly with the manganate and forms potassium permanganate, without precipitating manganese dioxide, 2K_{2}MnO_{4} + O + H_{2}O = 2KMnO_{4} + 2KHO. Thus a solution of potassium manganate undergoes a very characteristic change in colour and passes from green to red; hence this salt received the name of _chameleon mineral_.[22]

[21] Volume I. p. 157, Note 7.

[22] It was known to the alchemists by this name, but the true
explanation of the change in colour is due to the researches of
Chevillot, Edwards, Mitscherlich, and Forchhammer. The change in
colour of potassium manganate is due to its instability and to its
splitting up into two other manganese compounds, a higher and a
lower: 3MnO_{3} = Mn_{2}O_{7} + MnO_{2}. Manganese trioxide is
really decomposed in this manner by the action of water (see
later): 3MnO_{3} + H_{2}O = 2MnHO_{4} + MnO_{2} (Franke, Thorpe,
and Humbly). The instability of the salt is proved by the fact of
its being deoxidised by organic matter, with the formation of
manganese dioxide and alkali, so that, for instance, a solution of
this salt cannot be filtered through paper. The presence of an
excess of alkali increases the stability of the salt; when heated
it breaks up in the presence of water, with the evolution of
oxygen.

The method of preparing _potassium permanganate_ will be
understood from the above. There are many recipes for preparing
this substance, as it is now used in considerable quantities both
for technical and laboratory purposes. But in all cases the
essence of the methods is one and the same: a mixture of alkali
with any oxide of manganese (even manganous hydroxide, which may
be obtained from manganous chloride) is first heated in the
presence of air or of an oxidising substance (for the sake of
rapidity, with potassium chlorate); the resultant mass is then
treated with water and heated, when manganese dioxide is
precipitated and potassium permanganate remains in solution. This
solution may be boiled, as the liquid will contain free alkali;
but the solution cannot be evaporated to dryness, because a strong
solution, as well as the solid salt, is decomposed by heat.

By adding a dilute solution of manganous sulphate to a boiling
mixture of lead dioxide and dilute nitric acid, the whole of the
manganese may be converted into permanganic acid (Crum).

_Potassium permanganate_, KMnO_{4}, crystallises in well-formed, long red prisms with a bright green metallic lustre. In the arts the potash is frequently replaced by soda, and by other alkaline bases, but no salt of permanganic acid crystallises so well as the potassium salt, and therefore this salt is exclusively used in chemical laboratories. One part of the crystalline salt dissolves in 15 parts of water at the ordinary temperature. The solution is of a very deep _red colour_, which is so intense that it is still clearly observable after being highly diluted with water. In a solid state it is decomposed by heat, with evolution of oxygen, a residue consisting of the lower oxides of manganese and potassium oxide being left.[22 bis] A mixture of permanganate of potassium, phosphorous and sulphur takes fire when struck or rubbed, a mixture of the permanganate with carbon only takes fire when heated, not when struck. The instability of the salt is also seen in the fact that its solution is decomposed by peroxide of hydrogen, which at the same time it decomposes. A number of substances reduce potassium permanganate to manganese dioxide (in which case the red solution becomes colourless).[23] Many organic substances (although far from all, even when boiled in a solution of permanganate) act in this manner, being oxidised at the expense of a portion of its oxygen. Thus, a solution of sugar decomposes a cold solution of potassium permanganate. In the presence of an excess of alkali, with a small quantity of sugar, the reduction leads to the formation of potassium manganate, because 2KMnO_{4} + 2KHO = O + 2K_{2}MnO_{4} + H_{2}O. With a considerable amount of sugar and a more prolonged action, the solution turns brown and precipitates manganese dioxide or even oxide. In the oxidation of many organic bodies by an alkaline solution of KMnO_{4} generally three-eighths of the oxygen in the salt are utilised for oxidation: 2KMnO_{4} = K_{2}O + 2MnO_{2} + O_{3}. A portion of the alkali liberated is retained by the manganese dioxide, and the other portion generally combines with the substance oxidised, because the latter most frequently gives an acid with an excess of alkali. A solution of potassium iodide acts in a similar manner, being converted into potassium iodate at the expense of the three atoms of oxygen disengaged by two molecules of potassium permanganate.

[22 bis] The solution of this salt with an excess of impure commercial
alkali generally acquires a green tint.

[23] A solution of potassium permanganate gives a beautiful absorption
spectrum (Chapter XIII.) If the light in passing through this
solution loses a portion of its rays in it (if one may so account
for it), this is partially explained by the increased oxidising
power which the solution then acquires. We may here also remark
that a dilute solution of permanganate of potassium forms a
colourless solution with nickel salts, because the green colour of
the solution of nickel salts is complementary to the red. Such a
decolorised solution, containing a large proportion of nickel and
a small proportion of manganese, decomposes after a time, throws
down a precipitate, and re-acquires the green colour proper to the
nickel salts. The addition of a solution of a cobalt salt
(rose-red) to the nickel salt also destroys the colour of both
salts.

_In the presence of acids, potassium permanganate acts as an oxidising agent_ with still greater energy than in the presence of alkalis. At any rate, a greater proportion of oxygen is then available for oxidation, namely, not 3/8, as in the presence of alkalis, but 5/8, because in the first instance manganese dioxide is formed, and in the second case manganous oxide, or rather the salt, MnX_{2}, corresponding with it. Thus, for instance, in the presence of an excess of sulphuric acid, the decomposition is accomplished in the following manner: 2KMnO_{4} + 3H_{2}SO_{4} = K_{2}SO_{4} + 2MnSO_{4} + 3H_{2}O + 5O. This decomposition, however, does not proceed directly on mixing a solution of the salt with sulphuric acid, and crystals of the salt even dissolve in oil of vitriol without the evolution of oxygen, and this solution only decomposes by degrees after a certain time. This is due to the fact that sulphuric acid liberates free permanganic acid from the permanganate,[24] which acid is stable in solution. But if, in the presence of acids and a permanganate, there is a substance capable of absorbing oxygen--for instance, capable of passing into a higher grade of oxidation--then the reduction of the permanganic acid into manganous oxides sometimes proceeds directly at the ordinary temperature. This reduction is very clearly seen, because the solutions of potassium permanganate are red whilst the manganous salts are almost colourless. Thus, for instance, nitrous acid and its salts are converted into nitric acid and decolorise the acid solution of the permanganate. Sulphurous anhydride and its salts immediately decolorise potassium permanganate, forming sulphuric acid. Ferrous salts, and in general salts of lower grades of oxidation capable of being oxidised in solution, act in exactly the same manner. Sulphuretted hydrogen is also oxidised to sulphuric acid; even mercury is oxidised at the expense of permanganic acid, and decolorises its solution, being converted into mercuric oxide. Moreover, the end point of these reactions may easily be seen, and therefore, having first determined the amount of active oxygen in one volume of a solution of potassium permanganate, and knowing how many volumes are required to effect a given oxidation, it is easy to determine the amount of an oxidisable substance in a solution from the amount of permanganate expended (Marguerite's method).

[24] If sulphuric acid is allowed to act on potassium permanganate
without any special precautions, a large amount of oxygen is
evolved (it may even explode and inflame), and a violet spray of
the decomposing permanganic acid is given off. But if the pure
salt (_i.e._ free from chlorine) be dissolved in pure well-cooled
sulphuric acid, without any rise in temperature, a green-coloured
liquid settles at the bottom of the vessel. This liquid does not
contain any sulphuric acid, and consists of permanganic anhydride,
Mn_{2}O_{7} (Aschoff, Terreil). It is impossible to prepare any
considerable quantity of the anhydride by this method, as it
decomposes with an explosion as it collects, evolving oxygen and
leaving red oxide of manganese. _Permanganic anhydride_,
Mn_{2}O_{7}, in dissolving in sulphuric acid, gives a green
solution, which (according to Franke, 1887) contains a compound
Mn_{2}SO_{10} = (MnO_{3})_{2}SO_{4}--that is, sulphuric acid in
which both hydrogens are replaced by the group MnO_{3}, which is
combined with OK in permanganate of potassium. This mixture with a
small quantity of water gives Mn_{2}O_{7}, according to the
equation: (MnO_{3})_{2}SO_{4} + H_{2}O = H_{2}SO_{4} +
Mn_{2}O_{7}, and when heated to 30° it gives _manganese trioxide_,
(MnO_{3})_{2}SO_{4} + H_{2}O = 2MnO_{2} + H_{2}SO_{4} + O. Pure
manganese trioxide is obtained if the solution of
(MnO_{3})_{2}SO_{4} be poured in drops on to sodium carbonate.
Then, together with carbonic anhydride, a spray of manganese
trioxide passes over, which may be collected in a well-cooled
receiver, and this shows that the reaction proceeds according to
the equation: (MnO_{3})_{2}SO_{4} + Na_{2}CO_{3} = Na_{2}SO_{4} +
2MnO_{3} + CO_{2} + O (Thorpe). The trioxide is decomposed by
water, forming manganese dioxide and a solution of _permanganic
acid_: 3MnO_{3} + H_{2}O = MnO_{2} + 2HMnO_{4}. The same acid is
obtained by dissolving permanganic anhydride in water.

Barium permanganate when treated with sulphuric acid gives the
same acid. This barium salt may be prepared by the action of
barium chloride on the difficultly soluble silver permanganate,
AgMnO_{4}, which is precipitated on mixing a strong solution of
the potassium salt with silver nitrate. The solution of
permanganic acid forms a bright red liquid which reflects a dark
violet tint. A dilute solution has exactly the same colour as that
of the potassium salt. It deposits manganese dioxide when exposed
to the action of light, and also when heated above 60°, and this
proceeds the more rapidly the more dilute the solution. It shows
its oxidising properties in many cases, as already mentioned. Even
hydrogen gas is absorbed by a solution of permanganic acid; and
charcoal and sulphur are also oxidised by it, as they are by
potassium permanganate. This may be taken advantage of in
analysing gunpowder, because when it is treated with a solution of
potassium permanganate, all the sulphur is converted into
sulphuric acid and all the charcoal into carbonic anhydride.
Finely-divided platinum immediately decomposes permanganic acid.
With potassium iodide it liberates iodine (which may afterwards be
oxidised into iodic acid) (Mitscherlich, Fromherz, Aschoff, and
others). Ammonia does not form a corresponding salt with free
permanganic acid, because it is oxidised with evolution of
nitrogen. The oxidising action of permanganic acid in a strong
solution may be accompanied by flame and the formation of violet
fumes of permanganic acid; thus a strong solution of it takes fire
when brought into contact with paper, alcohol, alkaline sulphides,
fats, &c.

We may add that, according to Franke, 1 part of potassium
permanganate with 13 parts of sulphuric acid at 100° gives brown
crystals of the salt Mn_{2}(SO_{4})_{3},H_{2}SO_{4},4H_{2}O, which
gives a precipitate of hydrated manganese dioxide, H_{2}MnO_{3} =
MnO_{2}H_{2}O, when treated with water.

Spring, by precipitating potassium permanganate with sodium
sulphite and washing the precipitate by decantation, obtained a
soluble colloidal manganese oxide, whose composition was the mean
between Mn_{2}O_{3} and MnO_{2}--namely,
Mn_{2}O_{3},4(MnO_{2}H_{2}O).

The oxidising action of KMnO_{4}, like all other chemical reactions, is not accomplished instantaneously, but only gradually. And, as the course of the reaction is here easily followed by determining the amount of salt unchanged in a sample taken at a given moment,[25] the oxidising reaction of potassium permanganate, in an acid liquid, was employed by Harcourt and Esson (1865) as one of the first cases for the investigation of the laws of the _rate of chemical change_[26] as a subject of great importance in chemical mechanics. In their experiments they took oxalic acid, C_{2}H_{2}O_{4}, which in oxidising gives carbonic anhydride, whilst, with an excess of sulphuric acid, the potassium permanganate is converted into manganous sulphate, MnSO_{4}, so that the ultimate oxidation will be expressed by the equation: 5C_{2}H_{2}O_{4} + 2MnKO_{4} + 3H_{2}SO_{4} = 10CO_{2} + K_{2}SO_{4} + 2MnSO_{4} + 8H_{2}O. The influence of the relative amount of sulphuric acid is seen from the annexed table, which gives the measure of reaction _p_ per 100 parts of potassium permanganate, taken four minutes after mixing, using n molecules of sulphuric acid, H_{2}SO_{4}, per 2KMnO_{4} + 5C_{2}H_{2}O_{4}:

_n_ = 2 4 6 8 12 16 22
_p_ = 22 36 51 63 77 86 92

showing that in a given time (4 minutes) the oxidation is the more perfect the greater the amount of sulphuric acid taken for given amounts of KMnO_{4} and C_{2}H_{2}O_{4}. It is obvious also that the temperature and relative amount of every one of the acting and resulting substances should show its influence on the relative velocity of reaction; thus, for instance, direct experiment showed the influence of the admixture of manganous sulphate. When a large proportion of oxalic acid (108 molecules) was taken to a large mass of water and to 2 molecules of permanganate 14 molecules of manganous sulphate were added, the quantity x of the potassium permanganate acted on (in percentages of the potassium permanganate taken) in t minutes (at 16°) was as follows:

_t_ = 2 5 8 11 14 44 47 53 61 68
_x_ = 5·2 12·1 18·7 25·1 31·3 68·4 71·7 75·8 79·8 83·0

These figures show that the rate of reaction--that is, the quantity of permanganate changed in one minute--decreases proportionally to the decrease in the amount of unchanged potassium permanganate. At the commencement, about 2·6 per cent. of the salt taken was decomposed in the course of one minute, whilst after an hour the rate was about 0·5 per cent. The same phenomena are observed in every case which has been investigated, and this branch of theoretical or physical chemistry, now studied by many,[27] promises to explain the course of chemical transformations from a fresh point of view, which is closely allied to the doctrine of affinity, because the rate of reaction, without doubt, is connected with the magnitude of the affinities acting between the reacting substances.

[25] For rapid and accurate determinations of this kind, advantage is
taken of those methods of chemical analysis which are known as
'titrations' (volumetric analysis), and consist in measuring the
volume of solutions of known strength required for the complete
conversion of a given substance. Details respecting the theory and
practice of titration, in which potassium permanganate is very
frequently employed, must be looked for in works on analytical
chemistry.

[26] The measurements of velocity and acceleration serve for
determining the measure of forces in mechanics, but in that case
the velocities are magnitudes of length or paths passed over in a
unit of time. The velocity of chemical change embodies a
conception of quite another kind. In the first place, the
velocities of reactions are magnitudes of the masses which have
entered into chemical transformations; in the second place, these
velocities can only be relative quantities. Hence the conception
of 'velocity' has quite a different meaning in chemistry from what
it has in mechanics. Their only common factor is time. If _dt_ be
the increment of time and _dx_ the quantity of a substance changed
in this space of time, then the fraction (or quotient) _dx/dt_
will express the rate of the reaction. The natural conclusion,
come to both by Harcourt and Esson, and previously to them (1850)
by Wilhelmj (who investigated the rate of conversion, or
inversion, of sugar in its passage into glucose), consists in
establishing that this velocity is proportional to the quantity of
substances still unchanged--_i.e._ that _dx/dt_ = C(A - _x_),
where C is a constant coefficient of proportionality, and where A
is the quantity of a substance taken for reaction at the moment
when _t_ = 0 and _x_ = 0--that is, at the beginning of the
experiment, from which the time _t_ and quantity _x_ of substance
changed is counted. On integrating the preceding equation we
obtain log(A/(A - _x_)) = _kt_, where _k_ is a new constant, if we
take ordinary (and not natural) logarithms. Hence, knowing A, _x_,
and _t_, for each reaction, we find _k_, and it proves to be a
constant quantity. Thus from the figures cited in the text for the
reaction 2KMnO_{4} + 108C_{2}H_{2}O_{4} + 14MnSO_{4}, it may be
calculated that _k_ = 0·0114; for example, _t_ = 44, _x_ = 68·4 (A
= 100), whence _kt_ = 0·5004 and _k_ = 0·0114, (_see also_ Chapter
XIV., Note 3, and Chapter XVII., Note 25 bis).

[27] The researches made by Hood, Van't Hoff, Ostwald, Warder,
Menschutkin, Konovaloff, and others have a particular significance
in this direction. Owing to the comparative novelty of this
subject, and the absence of applicable as well as indubitable
deductions, I consider it impossible to enter into this province
of theoretical chemistry, although I am quite confident that its
development should lead to very important results, especially in
respect to chemical equilibria, for Van't Hoff has already shown
that the limit of reaction in reversible reactions is determined
by the attainment of equal velocities for the opposite reactions.