SURFACE ACTION 63 



that adsorbed at saturation. A and K are constants. In the case of acetic 

 acid and charcoal, this formula gives correct values for all concentrations of 

 acid between 1 and 3,000. 



The reason for taking saturation into account is that a surface already 

 completely covered cannot take up any more substance, since no change of 

 surface energy would result. This fact is found to be in agreement with 

 experimental data. 



In Schmidt's equation the constant S expresses the maximum amount adsorbed in satura- 

 tion, and A refers to the amount adsorbed at a particular concentration. Now, Arrhenius 

 points out (1912, p. 31) that the product of S and A in Schmidt's experiments is, within 

 the limits of experimental error, equal to the reciprocal of log, 10 or 0'4343. If this is so, 

 Schmidt's equation amounts to the integral of the following differential equation : 



da, 1 S a 

 ~dc = K* ~^' 



-where c is the concentration. This represents, in a simple form, how the amount adsorbed in 

 different concentrations is inversely proportional to the amount already adsorbed (a), and 

 xlirectly proportional to the distance from the point of saturation (S - a). Arrhenius finds that 

 the phenomena of adsorption follow very closely this formula, except in the cases where the 

 amount adsorbed is very small, on account of the large value of the heat of adsorption for the 

 first quantities adsorbed (Arrhenius, 1912, p. 37). Titoff (1910, p. 659) finds for nitrogen 

 the heat of adsorption per cubic centimetre of adsorbed gas, for the first small amounts, 

 0'373 gram-calorie, and when nearly saturated, 0'203 gram-calorie. For small values of 

 , in fact, the isotherms giving log a as a function of log p ( = concentration), instead of 

 being straight lines, diverge until they cut the axes of co-ordinates at 45, thus obeying 

 the law of Henry. 



If a process is found experimentally to be best expressed by parabolic 

 formulae of the kind given above, the conclusion must not be drawn hastily 

 that it is an adsorption. Other facts must be taken into consideration. For 

 instance, suppose a substance is soluble in two immiscible solvents in contact 

 with one another, but to a greater degree in one than in the other, it will 

 be distributed in a certain ratio between the two, this ratio being known as 

 the partition coefficient. If the dissolved substance is in single molecules in 

 both solvents, as succinic acid in ether and water, a simple linear relationship 

 holds, whatever the concentration. But, if the substance is associated in one 

 of the solvents, so that the number of the molecules is halved or otherwise 

 diminished, as in the case of benzoic acid, which is bitnolecular in benzene, 

 the ratio is no longer a linear one, but an exponential one, e.g., in the case 

 of benzoic acid in water and benzene, the concentration in water is equal 

 to the square root of the concentration in benzene (Nernst, 1911, pp. 495-498). 

 We see that the concentration of a substance in one phase may vary as a 

 power of that in the other phase. If we find, then, that n in the Freundlich 

 formula works out in a particular case to be a whole number, say 2, it might 

 be a simple case of partition between two solvents, in one of which the 

 substance is bimolecular. It is obvious that no difficulty arises when the 

 exponent is such as to be an impossible one, except as an adsorption. Such is 

 the case when it would imply the existence of fractions of molecules in one of 

 the solvents. In the case of the adsorption of arsenious acid by freshly pre- 

 cipitated ferric hydroxide, as investigated by Biltz, the exponent is one-fifth. As 

 Nernst points out (1911, p. 499), if this were a case of distribution between 

 solvents, arsenious acid must have a molecular weight in ferric hydroxide one- 

 fifth of that which it has in water. But in water it is already in single mole- 

 cules. Again, as is pointed out by Philip (1910, p. 227), the concentration of 

 carbon dioxide on charcoal increases proportionally to the cube root of the 

 pressure in the experiments of Travers (1907). If this were a case of solution 

 in charcoal, the carbon dioxide must have a molecular weight in the charcoal 

 one third of that in the gaseous state, which is not possible. The gas is 

 evidently condensed on the surface. 



Arrhenius ("Medd. k. Vetenskaps akad. Nobel institut," [2], No 7, 1910, quoted by 

 Marc, 1913) has proposed a simple formula, to apply to the adsorption of gases by charcoal. 

 It is pointed out that the compressibility of gases obeys the same formula ; adsorption is 

 regarded, accordingly, as a purely molecular property of the adsorbed matter and not as a 

 surface phenomenon. It appears, however, from the work of Marc (1913) that the formula of 



