28 Chapter III 



The equation which gave us this hyperbola was 



For any value of p there can be only one value of CR so long- 

 as K, which we have already described as a constant, remains in- 

 variable. 



To go back one stage further K itself involved three other 

 expressions which were also treated as constant a, the amount 

 of oxygen which is dissolved in 1 c.c. of water at 760 mm., and k 

 and k', the velocity constants of the forward and backward phases 



of the reaction 



2 ^ HbO 2 . 



Now in treating all these expressions as constants, as we have 

 already done, we have made the assumption that the temperature is 

 constant, for in reality they all vary with the temperature. Take 

 the simplest of them for instance, a; it is known that the amount 

 of oxygen dissolved in the solution varies inversely with the absolute 

 temperature. The changes of k and k' with the temperature are not 

 exactly known, but are certainly large. 



But concerning the relation of K (which only involves the ratio of 

 k to k') to temperature a great deal is known. Our knowledge of the 

 subject is due chiefly to van 't Hoff and Arrhenius. So far from 

 being a chance affair the relation of this expression K to changes 

 of temperature depends upon such fundamental properties of the 

 substance as the amount of heat given out when haemoglobin and 

 oxygen unite. That they do unite with the evolution of heat is clear 

 from an application of the principle of Le Chatelier to the fact that 

 to heat oxyhaemoglobin tends to dissociate it. That is to say, if at 

 38 C. and at 20 mm. O 2 pressure we have 71 % of the haemoglobin 

 as oxyhaemoglobin, then at a higher temperature, say 49 C., and the 

 same pressure a less percentage of the haemoglobin will be oxyhaemo- 

 globin and a greater quantity reduced haemoglobin. 



The law of van 't Hoff (1) relating the values K l and K for any 

 temperatures T l and T z is 



-q 2'a-Tx 



K z = K,e 2 T ^ , 



e being the base of the Napierian system of logarithms, and q the 

 heat evolved when one gram-molecule of haemoglobin unites with 

 one gram-molecule of oxygen. 



