THE PROBLEMS OF SOLUTION 99 



volume of the solvent. The nature of the inter- 

 action which occurs between the solute and the 

 solvent is unknown, possibly unknowable; but, 

 whatever it may be, each particle of solute 

 will affect only a minute sphere of solvent lying 

 round it. The solution, then, may be regarded 

 as containing a number of little systems, each 

 composed of a solute particle surrounded by an 

 atmosphere of solvent in some way influenced by 

 its nucleus. 



While the solution is concentrated, the little 

 spheres will intersect each other, and the addition 

 of further solvent will involve some change in the 

 interaction between solute and solvent. But, in 

 the process of dilution, a time will come when the 

 spheres are beyond each other's reach, and the 

 addition of more solvent merely increases their 

 mutual separation without affecting their internal 

 structure. 



Thus, in a dilute solution, the energy-change 

 of further dilution is merely the energy-change 

 involved in separating the particles of the solute ; 

 it will not depend on the nature of any possible 

 interaction between the solute and the solvent. 

 The change of energy is thus independent of 

 the nature of the solvent, and will be the same 

 whether that solvent be water, alcohol, or any 

 other liquid. It will even be the same when, 

 in cases where that is possible, the solvent is 

 removed altogether, and the solute is obtained 

 in the gaseous state. 



If we imagine that the bottom of a frictionless 

 engine cylinder is made of a semi-permeable mem- 

 brane, separating a solution within the cylinder 

 from a solvent without, it is easy to see that 



