# How to use *Vapour-pressure* in a sentence

Thermodynamic theory also indicates a connexion between the osmotic pressure of a solution and the depression of its freezing point and its

**vapour pressure**compared with those of the pure solvent.We can calculate the heat of formation from its ions for any substance dissolved in a given liquid, from a knowledge of the temperature coefficient of ionization, by means of an application of the well-known thermodynamical process, which also gives the latent heat of evaporation of a liquid when the temperature coefficient of its

**vapour pressure**is known.In contact with a solvent a metal is supposed to possess a definite solution pressure, analogous to the

**vapour pressure**of a liquid.When the components are completely immiscible, the

**vapour pressure**of the one is not influenced by the presence of the other.The composition of the distillate is determinate (by Avogadro's law) if the molecular weights and

**vapour pressure**of the components at the temperature of distillation be known.AdvertisementIn general, when the substance to be distilled has a

**vapour pressure**of only 10 mm.On distilling such a mixture under constant pressure, a mixture of the two components (of variable composition) will come over until there remains in the distilling flask the mixture of minimum

**vapour pressure**.The elevation of the boilingpoint is of little practical importance, but the reduction of

**vapour pressure**means that sea-water evaporates more slowly than fresh water, and the more slowly the higher the salinity.We then have water and vapour in equilibrium, and, as more heat enters, the temperature rises and the vapour-pressure rises with it.

If all the ice be melted, we pass along the

**vapour pressure**curve of water OA.AdvertisementIf all the water be frozen, we have the

**vapour pressure**curve of ice OB; while, if the pressure be raised, so that all the vapour vanishes, we get the curve OC of equilibrium between the pressure and the freezing point of water.If the supply of ice fails first the temperature will rise, and, since solid salt remains, we pass along a curve OA giving the relation between temperature and the

**vapour pressure**of the saturated solution.The

**vapour pressure**of a solution may be Pressure.The loss in the solution bulbs gives the mass of solvent absorbed from the solution, and the loss in the solvent bulbs the additional mass required to raise the

**vapour pressure**in the air-current to equilibrium with the pure solvent.The relative lowering of

**vapour pressure**of the solution compared with that of the solvent is measured by the ratio of the extra mass absorbed from the solvent bulbs to the total mass absorbed from both series of bulbs.AdvertisementThe

**vapour pressure**of the solution of a non-volatile solute is less than the**vapour pressure**of the pure solvent.If the height be not too great, we may assume the density of the vapour to be uniform, and write the difference in

**vapour pressure**at the surfaces of the solvent and of the solution as p - p' = hgo-.When the solution and solvent are in equilibrium across the partition, the

**vapour pressure**of the solution has been increased by the application of pressure till it is equal to that of the solvent.In any solution, then, the osmotic pressure represents the excess of hydrostatic pressure which it is necessary to apply to the solution in order to increase its

**vapour pressure**to an equality with that of the solvent in the given conditions.Similar 'considerations show that, since at its freezing point the

**vapour pressure**of a solution must be in equilibrium with that of ice, the depression of freezing point produced by dissolving a substance in water can be calculated from a knowledge of the**vapour pressure**of ice and water below the freezing point of pure water.AdvertisementAnother verification may be obtained from the phenomena of

**vapour pressure**.Here n is the number of gramme-molecules of solute, T the absolute temperature, R the gas constant with its usual "gas" value, p the

**vapour pressure**of the solvent and v1 the volume in which one gramme-molecule of the vapour is confined.In the

**vapour pressure**equation p - p' = Pa/p, we have the vapour density equal to M/v 1, where M is the molecular weight of the solvent.Substituting these values, we find that the relative lowering of

**vapour pressure**in a very dilute solution is equal to the ratio of the numbers of solute and solvent molecules, or (p - p')/p = n/N.Dilute solutions of substances such as cane-sugar, as we have seen, give experimental values for the connected osmotic properties - pressure, freezing point and

**vapour pressure**- in conformity with the theoretical values.AdvertisementThe osmotic pressure (defined as the difference in the hydrostatic pressures of the solution and solvent when their vapour pressures are equal and they are consequently in equilibrium through a perfect semi-permeable membrane) may also depend on the absolute values of the hydrostatic pressures, as may the

**vapour pressure**of the liquids.To investigate the osmotic pressure of a' strong solution we may consider the hydrostatic pressure required to increase its

**vapour pressure**to an equality with that of the solvent.The relation between hydrostatic pressure and the

**vapour pressure**of a pure liquid may be obtained at once by considering the rise of liquid in a capillary tube.The difference in

**vapour pressure**at the top and at the bottom of the column is p - p' = Pclp, as shown above for a column of solution.Callendar has shown that the variation of

**vapour pressure**of a solution with pressure is given by the expression V'dP = vdp, where V' is the change in volume of the solution when unit mass of solvent is mixed with it.The relation between the equilibrium pressures P and P' for solution and solvent corresponding to the same value po of the

**vapour pressure**is obtained by integrating the equation V'dP' = vdp between corresponding limits for solution and solvent.J p J where p and p' are the vapour pressures of solvent and solution each under its own

**vapour pressure**only.From this equation the osmotic pressure Po required to keep a solution in equilibrium as regards its vapour and through a semi-permeable membrane with its solvent, when that solvent is under its own

**vapour pressure**, may be calculated from the results of observations on**vapour pressure**of solvent and solution at ordinary low hydrostatic pressures.The slope of the temperature

**vapour pressure**curves in the neighbourhood of the freezing point of the solvent is given by the latest heat equation.Whether osmotic pressure be due to physical impact or to chemical affinity it must necessarily have the gas value in a dilute solution, and be related to

**vapour pressure**and freezing point in the way we have traced.The fundamental phenomenon they take to be the identity of

**vapour pressure**, and consider the combination necessary to reduce the**vapour pressure**of a solution to the right value.If each molecule of the solute combines with a certain number of molecules of the solvent in such a way as to render them inactive for evaporation, we get a lowering of

**vapour pressure**.If there are n molecules of solute to N of solvent originally, and each molecule of solute combines with a molecule of solvent, we get for the ratio of vapour pressures p/p'=(N - an)/(N - an+n), while the relative lowering of

**vapour pressure**is (p - p')/p=n/(N - an).This temperature is somewhat different from the ordinary melting-point, the latter corresponding to atmospheric pressure, the former to the maximum vapour-pressure; and so we come to a third relation for polymorphism.

Babo, 1847, gave the law known by his name, that the " relative lowering" (p - po)lpo of the vapour-pressure of a solution, or the ratio of the diminution of vapour-pressure (p - po) to the vapour-pressure po of the pure solvent at the same temperature, was constant, or independent of the temperature, for any solution of constant strength.

At the freezing-point, the solution must have the same vapour-pressure as the solid solvent, with which it is in equilibrium.

The relation follows immediately from Kirchhoff's expression (below, section 14) for the difference of vapour-pressure of the liquid and solid below the freezing-point.

In this case the ratio of the vapour-pressure of the solution p" to that of the solvent p' should be equal to the ratio of the number of free molecules of solvent N - an to the whole number of molecules N - an+n in the solution.

The explanation of this relation is that each of the n compound molecules counts as a single molecule, and that, if all the molecules were solvent molecules, the vapour-pressure would be p', that of the pure solvent.

Arrhenius, by reasoning similar to that of section 5, applied to an osmotic cell supporting a column of solution by osmotic pressure, deduced the relation between the osmotic pressure P at the bottom of the column and the vapour-pressure p" of the solution at the top, viz.

It is probable that osmotic pressure is not really of the same nature as gas-pressure, but depends on equilibrium of vapour-pressure.

The vapourmolecules of the solvent are free to pass through the semi-permeable membrane, and will continue to condense in the solution until the hydrostatic pressure is so raised as to produce equality of vapour-pressure.

The highest pressures recorded for cane-sugar are nearly three times as great as those given by van't Hoff's formula for the gas-pressure, but agree very well with the vapour-pressure theory, as modified by Callendar, provided that we substitute for V in Arrhenius's formula the actual specific volume of the solvent in the solution, and if we also assume that each molecule of sugar in solution combines with 5 molecules of water, as required by the observations on the depression of the freezing-point and the rise of the boiling-point.

As a matter of fact, the two terms A+B/0 are the most important in the theoretical expression for the vapour-pressure given below.

If we assume formulae of the simple type A+B/0 for two different substances which have the same vapour-pressure p at the absolute temperatures 0' and 0" respectively, we may write log p=A'+B'/0'= A"+B"/0", .

The empirical formulae above quoted must be compared and tested in the light of the theoretical relation between the latent heat and the rate of increase of the vapour-pressure (dp/d0), which is given by the second law of thermodynamics, viz.

The formula evidently applies to the vapour-pressure of the pure solvent as a special case, but Kirchhoff himself does not appear to have made this particular application of the formula.

In the paper which immediately follows, he gives the oft-quoted expression for the difference of slope (dp/d9) 8 -(dp/de) 1 of the vapour-pressure curves of a solid and liquid at the triple point, which is immediately deducible from (21), viz.

A liquid boils when its

**vapour pressure**equals the superincumbent pressure (see Vaporization); consequently any process which diminishes the external pressure must also lower the boiling-point.The phenomena of solution and of

**vapour pressure**constitute cases of equilibrium, and conform to the laws deduced by Gibbs, which thus yield a valuable method of investigating and classifying the equilibria of solutions.The relative lowering of the vapour-pressure can be easily measured by Dalton's method of the barometer tube for solvents such as ether, which have a sufficient vapour-pressure at ordinary temperatures.