26 LAWS OF AVOGADRO AND VAN'T HOFF. chap. at 0° and 760 mm. pressure ; • under these conditions (r= 273, p = 1033'6 grams per square centimetre) the
volume of 1 gram is /r-n/^T^ioTrPi = 699*3 c.c. and that of
32 grams is 32 x 6993 c.c. ; consequently —
1,033-6 X 32 X 699-3 = 273^
R = 84,688.
If the pressure is measured not in grams per square centimetre, but in millimetres of mercury, the value of R is 1-36 times smaller, i,e, R = 62,265.
We have already obtained (see p. 13) another expression of Avogadro's rule, extremely useful for calculations, namely —
pv=:2TcQ[,
in which the value of -B is 2 (or, more exactly, 1'99).
By means of this equation we can ascertain the pressure, volume, or temperature of a given mass of gas provided we know two of these factors.
It might be required to find, for example, how many litres of saturated water vapour are evolved from 1 litre of water at 0°. The vapour tension of water at this tem- perature is 460 mm. In our formula, pv = RT, we have to set p = 4-6, R = 62,265, and T = 273, and we find v = grams, of water. A litre of water at 0° weighs 9999 grams, and contains, therefore, 55-55 gram-molecules ; consequently, in the state of gas it occupies a volume 55*55 times as great as that which we have calculated for 1 gram-molecule, 55*55 X 3,612,000 c.c. = 205,600 litres.
Law of van der Waals. — The relationship pv = RT represents a limit law — that is to say, it only becomes strictly correct at very great dilution. At moderate and high pressures the forces acting between the molecules, and the volume actually occupied by the molecules, become
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