144 



CHEMICAL TRANSFORMATIONS IN 



The difference in volume energy before and after the reaction 

 cannot be obtained by taking the differences in the total osmotic 

 pressures before and after the reaction, because the quantity of 

 substance appearing is not brought during the change from the 

 one of these pressures to the other, but from the zero of pressure 

 to the pressure at which it is finally found in the reaction that 

 is, to the partial pressure of the component substance to which 

 it belongs ; and similarly the grm. molecule of substance disappearing 

 passes from the partial pressure at which that substance happens 



to be present in solution to 

 zero pressure. Hence the 

 amount of volume energy must 

 be obtained separately for each 

 substance taking part in the 



\ 



Q 



reaction. 



This amount of energy may 

 be obtained as follows : Suppose 

 a definite amount of a substance 

 to be in solution in a semiperme- 

 able cylinder fitted with a semi- 

 permeable piston, as sketched 

 in the diagram, and surrounded 

 by solvent. Then if the pres- 

 sure on the piston be changed, 

 just as in the case of a gas, the 

 solution will correspondingly 

 change in volume. The work 

 done by the dissolved substance 

 or solute is PoTV, where P is the 



pressure and dV the small change in the volume. Or, using the gas 

 law PV = RT, we have on differentiation PcZV = - WP, and again 



prp 7p 



since V= p , PdV = RT p -. On integrating this yields for the work 



done by the gas in expanding isothermally from pressure P x to 



p 



pressure P 2 the well-known expression "W = RT log -p 1 . 



"2 



This amount of work may be expressed' as heat energy by giving 

 the proper value to the constant RT, which for a grm. molecule of a 

 substance which obeys the gas law works out to 5-8 K calories 1 at C. 



1 The K (calory) is the amount of heat necessary to raise 1 grm. of 

 water from to 100 C., and is approximately equal to 100 grm. calories. 



FIG. 1 WORK DONE IN COMPRESSION 

 OF A SOLUTION IN A SEMI-PERMEABLE 

 CYLINDER. 



