98 Dr. 8. R. Milner on Surface Concentration, 

 Hence the surface excess is given by the equation 

 dr___rrd'p 

 dc~ c dc W 



By this equation a may always be calculated when the 



curve of the surface tension with the concentration is known* 



dp 

 If the osmotic pressure obeys the ordinary gas law, -J- = RT; 



but whether this is the case or not, it may always be 

 obtained from freezing-point measurements. If i stands 

 for the ratio of the molecular lowering of the freezing-point 

 (lowering per gram-mol. per litre) to the normal lowering 

 1*86, p = iJlTc, and consequently 



t=iRT+rav <7 /. 



dc dc 



When, as is usually the case, the variation of i with the 

 concentration is small, the second term of this equation may 

 be neglected in comparison with the first, and we have approxi- 

 mately from (3) 



' /t = -;rt' 7 (4) 



dc c 



In all inorganic solutions so far measured the surface tension 



dr . 

 increases linearly with the concentration, that is -y- is positive 



and constant; hence o- is negative, and - is constant, i. e., 



there is a defect of salt in the surface-film of an amount 

 proportional to the concentration. 



As regards the actual magnitude of the defect, sodium 

 chloride may be cited as an average case. The increase of 

 surface tension * is 1'72 dynes per cm. for an increase in 

 concentration of 1 gm.-inol. per litre. Also i — 1*74, taking an 

 average value of the factor, 11 = 8*32 x 10 7 ergs per degree C, 

 T = 290°. Substituting these numbers in (4) we obtain for a 

 normal solution, 



a= — 4"09 x 10" -11 gm.-mol. per sq. cm. 



This is equivalent to a defect of *024 mgm. per sq. metre. 



On the other hand, in several organic solutions the surface 

 tension is less than that of water, and there is consequently 

 an excess of solute in the surface. Acetic acid, the surface 

 tension of which has been measured by Whatmough f, forms 



* Torch, Ann. der Pki/sik, xvii. p. 744 (1905). 

 f Zeitfiir Phys. Chcm. xxxix. p. 166 (1902). 



