48 BOILING AND FREEZING POINT. chap.

If, then, by experiment the vapour pressure of the solvent has been determined for all temperatures, and thereby tan a has been found, we can calculate the rise of boiling point dT, knowing the value otp ^ p\ which is the relative lowering of the vapour pressure referred to in the preceding chapter.

The mechanical theory of heat gives us the following

formula (Clapeyron's equation) for y^ or for tan a —

dp _ \

��where T is the absolute temperature at which the vapour pressure is p, X is the heat of vaporisation of 1 gram- molecule of the solvent, and v and v\ are the volumes of the gram-molecule in the gaseous and liquid states. Compared with ?', vi is so small that without introducing an appreciable error it may be entirely omitted.

Further, we have the relationship —

pc = RT

(where p and v denote the pressure and volume of the gaseous solvent); and if this be introduced into the above equation, we obtain —

p-p' RT^ or— cfl= ' ^ .

p A

Since X is not measured in mechanical units but in calories, E also must be expre9sed in calories. The value of E in calories has already been shown (see pp. 13 and 26) to be equal to 1'99, for which, with a sufficiently close approxi- mation, we may set 2. For a solution which contains n dissolved molecules per 100 molecules of solvent, we know

that ^- - ^ = - - and for a solution which contjdns 7ii

gram-molecules of dissolved substance per litre, we have

�� �