JA C O B U S H. V A N’T HOFF
Osmotic pressure and chemical equilibrium
Nobel Lecture, December 13, 1901*
Although the investigations on which I am about to speak were carried out
15 years ago, I am going to begin by describing still earlier studies - those
which, in fact, formed the basis of my own. These studies concern the experimental
determination of osmotic pressure.
What is osmotic pressure? When a solution, e.g. of sugar in water, is
separated from the pure solvent − in this case water − by a membrane which
allows water but not sugar to pass through it, then water forces its way
through the membrane into the solution. This process naturally results in
greater pressure on that side of the membrane to which the water is penetrating,
i.e. to the solution side.
This pressure is osmotic pressure.
It is thanks to this osmotic pressure that the sap of the oak-tree rises to the
topmost twigs. This pressure was known to exist as long ago as the beginning
of the 19th century, but it is only somewhat more than 20 years ago since
this phenomenon has been the subject of precise measurements. It was the
botanist Pfeffer who first measured this pressure in 1877 by making a
membrane which satisfied the following three conditions: It was permeable
to water, impermeable to sugar, and it withstood the by no means negligible
pressure to which it was subjected.
Osmotic forces are in fact unexpectedly great: with a 1% sugar solution
they are equal to no less than 2/3 atm.
Thus, Pfeffer measured osmotic pressure but he was unable to find the
relation between the value of this pressure and the concentration of the solution,
its temperature, etc. He put this problem to the celebrated physicist
Clausius in Bonn, but he, too, failed to discover any regular interrelations.
Pfeffer’s results therefore remained in a specialized botanical paper, thus escaping
the notice of scientists in other fields.
The importance of a solution of this problem becomes clear when one
* The speaker is restricted in his choice of subject by the rules of the Nobel Foundation
and craves indulgence if he touches upon matters not suited to presentation in popular
form.
6 1901 J.H.VAN’T HOFF
remembers the vital role played by osmotic pressure in plant and animal life.
The membranes of the cell are in fact permeable to water but not to substances
dissolved in the cell fluid. Osmotic pressure can therefore develop in
the cells. It was the botanist Hugo de Vries in particular who emphasized its
importance to plant life: Such pressure (turgor) must exist in the plant cells,
if they are not to wither; in other words it is essential for growth. Thus,
plants wither not only when they lose water through evaporation but also
when they are surrounded by an aqueous solution of common salt, potassium
chloride, magnesium chloride, sugar or other substance, if the solution is of
higher osmotic pressure, whereas they do not wilt if the osmotic pressure is
lower. The critical point can be very accurately determined with the aid of a
microscope, and thus De Vries found a method of establishing how concentrated
a solution must be if it is to have the same osmotic pressure as the plant
cells, i.e. if it is to be "isotonic" with them.
Donders and Hamburger then discovered that osmotic pressure plays no
less important a part in animal than in plant life. The life of the higher animals
stands or falls with the erythrocytes. These are cells which in relation to
the osmotic pressure of the liquid surrounding them behave in a manner
similar to plant cells, i.e. if the external osmotic pressure is too great, then a
phenomenon similar to wilting occurs. And at that time it was particularly
remarkable that solutions found to be isotonic in this respect were also isotonic
for the plant cell.
Lastly, in chemistry osmotic pressure is very important because, among
other things, it can be related directly to what is known as chemical affinity.
In the binding of water of crystallization, for instance, one can imagine that
natural gypsum, the chemical formula of which is CaSO4· 2H2O, binds its
water of crystallization in almost the same way as the plant cell holds water
within itself, and the force with which this takes place can be measured in the
same way as De Vries measured the osmotic force of cells. If a piece of transparent
selenite is placed successively in aqueous solutions of increasing concentration
of any substance, then there finally comes a point at which the
gypsum can no longer retain its water but gives it up to the solution of
greater osmotic pressure: "it wilts". The force with which gypsum binds
its water can therefore be measured directly by osmotic pressure.
So much for the earlier work.
In the subsequent study of processes in this field the law around which the
prize-winning work centred was now discovered.
It was found namely that with sufficiently dilute solutions the osmotic
O S M O T I C P R E S S U R E A N D C H E M I C A L E Q U I L I B R I U M 7
pressure was the same as the gas pressure, i.e. the pressure which the dissolved
substance would exert as gas. To some extent this is obvious: Just as one
imagines the gas pressure P to arise as a result of the movement of molecules
and of their collisions with the walls (Fig. 1), so can one imagine the osmotic
pressure p to arise as a result of the collisions of the dissolved molecules
with the semi-permeable membrane (Fig. 2) surrounded by the solvent
(denoted by shading).
Fig.1. Fig.2.
However, independently of an anyway hypothetical conception on the cause
of this pressure, it was found that under the same circumstances, i.e. with the
same number of molecules in the same volume and at the same temperature,
the pressures also were the same. This can be expressed mathematically by
the equation
(1)
osmotic pressure = gas pressure. From this formula it is possible to calculate
theoretically the value found by Pfeffer: $ atm. for a 1% sugar solution.
It was found, however, that a relatively small group of solutions - all of
them aqueous - of acids, bases and salts, which are known as electrolytes, e.g.
solutions of sodium chloride or potassium chloride (i.e. mostly those which
were investigated first), constituted an exception. In the case of these the law
did not apply. The osmotic pressure was i times greater than the theoretical
value, and consequently the following formula was for a tune used for these
exceptions:
(2)
We shall be returning to this point later. In the case of the non-electrolytes
this reduces to (I), since i = 1. Now let us apply the basic relationship and
8 1901 J.H.VAN’T HOFF
consider the so-called chemical equilibrium. A distinction must be made between
complete and incomplete reactions, according to the final state in
which a chemical reaction results. After dynamite has been exploded not the
slightest trace of the original substance is found. The reaction is complete. In
other cases, however, the reaction ceases before complete transformationfor
instance, where methanol and formic acid are converted into water and
methyl formate according to the equation:
A similar formula might also be drawn up for the dynamite explosion. In
the reaction which has just been formulated, however, only $ of the possible
quantity of the products on the right side are formed. The reason for this is
that not only are methyl formate and water produced from methanol and
formic acid, but that conversely methanol and formic acid are produced
again from methyl formate and water. This can be illustrated in the formula
by introducing the sign for a reversible reaction instead of the sign of equality:
Such transformations, then, take place in either direction: the final state
being known as chemical equilibrium.
The laws governing this chemical equilibrium in the case of dissolved
substances can now be deduced by using the basic relationship for osmotic
pressure.
The first of these,
for non-electrolytes : (3a)
for electrolytes : (3b)
determines the quantity of the product which will form in a given volume
from given quantities with substances reacting with one another, provided
that a single so-called equilibrium constant, K, is known.
Since the value i enters into this formula in the case of electrolytes, we see
that it plays an important part in the relevant laws of equilibrium.
In the second law
(4)
O S M O T I C P R E S S U R E A N D C H E M I C A L E Q U I L I B R I U M 9
we find yet another factor affecting the equilibrium, namely the temperature
T (so-called absolute temperature). W is the quantity of heat evolved during
the reaction.
Finally, in the last formula
allowance is also made for the quantity of work done during a chemical reaction,
e.g. a dynamite explosion, the quantity being linked with the equilibrium
constants.
Following this brief mathematical excursion we will now turn to some of
the results which were subsequently obtained by means of these formulae.
I. The molecular weight of dissolved substances is now easy to determine.
Fifteen years ago it was possible to assess the molecular weight of gaseous
substances only. By means of osmotic pressure it is now also possible to determine
the molecular weight of dissolved substances. But it is not only
liquids which have come into the range of molecular weight determination.
In addition, homogeneous mixtures, e.g. isomorphic mixtures of solid substances
are comparable to solutions, and the laws of osmosis can therefore be
extended to solid substances. Consequently, it is now possible to determine
molecular weight not only in the gaseous, but also in the liquid and in the
solid state of aggregation. The problem of molecular weight determination
has thus to a certain extent been solved.
The results are very interesting. It has often been thought that during
the transition from the gaseous to the liquid phase several gas molecules unite
to form a liquid molecule, and that the molecules in the solid state of aggregation
consist of still larger complexes. In reality, however, the situation is
very simple. It is in fact only in exceptional cases that in a liquid or solid
state of aggregation, molecules consisting of two gas molecules of the substance
have been found, whereas nothing like a substance which forms aggregates
of three gas molecules has yet been found for certain.
II. Equation (2) was at first the critical point in the theory. I should not
have had the pleasure of giving this lecture if Professor Arrhenius had not
succeeded in demonstrating the cause of these exceptions and therefore in
reducing Equation (2) to (1).
III. We need go no further into Equation (3a). It coincides essentially with
the law of mass action formulated by the two Norwegians Guldberg and
10 1901 J. H.VAN’T HOFF
Waage, except with regard to i and n (number of molecules participating in
the reaction).
IV. Equation (4) links the chemical equilibrium constant K with the heat
W evolved by the reaction. It can of course be tested experimentally, and has
indeed been confirmed experimentally.
A corollary to this law shows how the chemical equilibrium varies with
temperature − namely how, as the temperature increases, more of the one
compound is formed at the expense of the other, or vice versa. This corollary
can be stated as follows: At low temperature the greater yield is always of
that product whose formation is accompanied by evolution of heat.
In most cases, in fact, the equilibrium at ordinary temperature has shifted
so far in favour of those products which are situated on one side of the arrows
in the chemical formula that no trace of the products on the other side can be
detected. An example of this is the formation of water from a mixture of
oxygen and hydrogen, the so-called oxyhydrogen gas. At ordinary temperature
the equilibrium is so much on the side of the water that the oxyhydrogen
gas cannot be detected at all. At higher temperatures there is a shift
towards the gas; a measurable equilibrium between water, oxygen, and hydrogen
is established. The above-mentioned formula thus embraces the dissociation
processes which were studied by Deville and Deprez.
V. It is only very recently that it has been possible to test Equation (5) experimentally.
Bredig and Knüpfer have determined K from the equilibrium
and have also determined by chemical methods the work done during the
reaction.
In conclusion a timely remark. Whereas application of the laws of osmosis
has proved very fruitful in the field of chemistry, what De Vries and Donders
emphasized 15 years ago, namely that osmotic pressure plays a fundamental
role in plant and animal life, has since been fully confirmed as well.
The determination of osmotic pressure and of the associated lowering of the
freezing-point of solutions is already frequently of great importance in
physiology and medicine, e.g. in the study of disease. However, the peculiar
discovery made very recently by Loeb is the most important one of all. This
scientist has been studying the problem of fertilization, which is bound up so
closely with the problem of life, and he has found that the eggs of sea urchins
will develop as a result of the temporary action of a specific osmotic pressure
brought about by solutions of potassium chloride, magnesium chloride,
sugar, etc.