38 CHEMICAL TRANSFORMATIONS 



rapidly drops. If now the value of C is negative, that is, if chemical 



energy is absorbed on change of substance A into substance B, then 



p 

 an equilibrium will be reached as soon as the value of - RT log =- 



A 



equals C. This will occur nearer X, as at E 1? if C has a large negative 



value than if C has a small negative value, as at E 2 . Beyond the 



p 

 point of equilibrium so defined the positive value of - RT log ^ B 



p 



becomes still smaller, and hence H, which is C - RT log ~, becomes 



*A 



negative ; that is, energy is absorbed, the reaction is endothermic, 



and cannot proceed without external energy being added, which is 

 excluded under the conditions we are considering. But if C has a 

 positive value the reaction will run farther towards X' before the 



equilibrium point is reached. As it so runs P B continually increases 



p 

 and P A decreases. So long as P A is greater than P B , the fraction p- 



p 



is less than unity, its logarithm is negative, and hence - RT log p- 



p 



has a positive value ; but at the position where P B = P A , log p B = log 1 = 0, 



and the curved line representing the change in the osmotic energy, 

 crosses the base line for the osmotic energy set free at this point in the 



reaction is zero. From this point onward osmotic energy is absorbed 



p 

 instead of being given out in the reaction, for log ^ now becomes positive 



*A 



and goes on increasing in value, at first slowly, and later very rapidly 

 as P A becomes very small in the neighbourhood of X' and the curved 

 line becomes asymptotic to the ordinate. Hence aba certain point the 

 distance of the curved line below the base line becomes equal to the 

 distance above the base line of the horizontal line representing the 

 positive value of C. Also the smaller the positive value of C the 

 further from the end point will be the point of equilibrium. 



The same reasoning applies if we start at X' with the substance 

 all in the form B, and proceed towards X. The diagram to suit 

 progress in this direction is the mirror reflex in the base line of 

 the one given for the opposite direction (X to X'). For if the 



value of C was positive in passing from A to B, it will be negative 



p 

 in passing from B to A, and value of - RT log ^ will be positive 



p 



at the X' end and negative at the X end, precisely as - RT log p- B 



was positive at the X end and negative at the X 7 end. Hence 

 the same equilibrium point is reached from whichever condition A or 



