Page:Proceedings of the Royal Society of London Vol 69.djvu/101

Rh VI. Contractions.

From the density determinations the contractions in the formation of 1 gramme of the acid solutions have been calculated. The volumes occupied by 1 gramme of water at the temperatures of 4, 14'2 and 24'2 are taken from Rosetti's tables as at 1, 1*00075 and 1*00268 c.c. respec- tively, while those of 100 per cent, acid are calculated with slight corrections from the density values obtained for the 99 '97 per cent, acid previously prepared. Owing to the difficulty experienced in elimina- ting the last fractions per cent, of water from the acid no attempts were made to obtain another sample ; therefore, if there had been an error in these density determinations the values for all the contractions would be uniformly increased or diminished, but the conclusions to J>e drawn therefrom not materially affected.

As it has been shown in the previous sections that from various causes differences in value occurred of some units in the fifth place of decimals in the density determinations, these figures were omitted as inconsequent for the purpose of calculation, and the results expressed in 1/100,000 c.c.

The results are calculated by means of the formula

c = pV/IQO + (100 -^)Vi/100 - V 2 ,

wherein p = percentage of acid, V = volume occupied by 1 gramme of acid, Vi = volume occupied by 1 gramme of water, and V 2 the reciprocal of the density for any particular mixture.

The details of one calculation are given for an example :

Percentage of acid = 61-53, of water = 38 -47. Volume occupied by 1 gramme of water at 14 '2 C. = 1 '00075 c.c.

Volume occupied by 1 gramme of 100 per cent, acid at 14 '2 C. = 0-65679 c.c.

/ "p.

Volume occupied by mixture I = - ) at 14' '2 C. 0-72383 c.c.

joV/100 = 0-40412 c.c. (100-j)Vi/100 = 0-38499 c.c.

Sum = 0-78911 c.c.

V 2 = 1/D = 0-72383 c.c. Contraction C = 0*06528 c.c. or 6528 x 10~ 5.