Forces on tlie Osmotic Pressure of Electrolytes, 747 



Putting 



q = 4-77 x 10- 10 e.s.u., e= 9654 x 3 x 10 10 e.s.u., 



R = 8'31 x 10 7 erg/deg. C, T = 273, K = 87 at 0° O, 



we get h =1-203 0*. 



Given the virial we can, i£ we may treat the electrolyte as 

 we should a gas, at once obtain the pressure by using the 

 equation of Clausius, which states that pressure X volume = 

 § (kinetic energy) — J (virial). Applied to a completely 

 dissociated electrolyte this gives, since there are two gram 

 ions present in the volume V, 



PV=2RT-JW 



jj«»-4*yw (5) 



or 



It may not, however, appear quite legitimate to apply with- 

 out question formulae deduced from the concepts of the 

 kinetic theory of gases directly to the complex phenomenon 

 which the osmotic pressure of an electrolyte undoubtedly is. 

 The same formula is therefore deduced below in another 

 way. 



When, as is the case in the system we are considering, 

 the internal forces vary according to the inverse square law, 

 the virial bears a simple relation to the internal potential 

 energy of the system. If we measure the internal energv, 

 U, of the solution at the volume V by the work which would 

 be done by the electrical forces if the ions of opposite 

 sign were allowed to collapse on each other in pairs from 

 the positions which they occupy in the volume V, — or in 

 other words by the heat which would be produced if 

 complete association of all the ions were brought about — and 

 if U^ stands for the corresponding energy of the system at 

 infinite dilution, then U^ — U is easily seen to be the average 



value of the summation of — ( + X^ I for all pairs of ions 



in the solution. This is the attractive virial W, and, in fact, 



u=u„-w 



=U„-RT/ t /(/<) 

 We can now apply the general thermodynamical relation 



dXJ _ T dP _ 



dV~ dT * "■*'•'"•" ' W 



