250 FREE ENERGY OF BIOLOGICAL PROCESSES 



Although we have sufhcient data from which to calculate the 

 entropies of CO2 and of H2O, there are no such data available for 

 mannite. We can, however, obtain an approximate value for our 

 present purpose by comparing its average atomic heat at 25°C. (the 

 only value found in the literature) with those of other substances 

 whose entropies are known and whose average atomic heats at 25°C. 

 are approximately of the same magnitude as that of the mannite. 

 For this purpose, we may plot C^ against log T for solid crystalline 

 CeHe and for graphite. Since for a certain class of substances these 

 curves do not intersect, but approach the absolute zero in the same 

 general way, we may locate between these two curves the average 

 atomic heat curve for mannite.^ 



The area under this curve amounts to approximately 0.95. This 

 multiplied by the number of atoms and by 2.3 (see Equation 2) gives 

 56.8 entropy units. Subtracting from this value the entropies of 14 

 hydrogen atoms (222.6), 6 oxygen atoms (144.6), and 6 carbon atoms 

 (7.8), we obtain —318 entropy units as the value of A5 for mannite. 

 We then have for the free energy of formation of 1 mol of soKd crys- 

 talline mannite from its elements at 25°C. 



AF = AH - TAS = -315,060 - (-94,760) = - 220,300 calories 



Finally to obtain the free energy of 1 mol of mannite when dissolved 

 in 10 kilos of water, we may assume, in the case of substances like 

 mannite, that the activities are proportional to the concentrations, 

 so that for the free energy of dilution from saturation to 0.1 molal 



1.49 



AF' = - RTln = - 1,600 calories 



0.1 



Adding this to the above value, we obtain —221,900 calories. With 

 this value we can now calculate the available or free energy of the 

 reaction. 



CsHhOb + 6§ O2 = 7 H2O + 6 CO2 

 or 



AF" = 7(-56,620) + 6(-94,360) - (-221,900) = - 740,600 calories 



* The average atomic heat for mannite is obtained by multiplying its specific 

 heat, which is given in the literature for 25°C., by the molecular weight and divid- 

 ing the product by the number of atoms in the molecule. 



