EFFECTS OF PRESSURE 843 



where JE is the change in internal energy. Thus: 



, ,, AE AS PAY 



and the variation of In K with the pressure is given by: 



d\nK _ AV 

 dP ~ W 



(15-107) 



which was originally obtained by van't Hoff. When the reaction involves 

 an increase in the volume, i.e., AV is positive, K will increase with rise 

 in the i^ressure, indicating an opposition to the reaction. If we represent 

 the dissociation constant at zero pressure as Kq: 



In K =\n Ko + —^^ (15-108) 



when the volume change is independent of the pressure, and: 



K = K,e^P-^^RT) (15-109) 



A plot of log K against P should then give a straight line with an intercept 

 of log Kq and a slope of z]F/2.303i?T. From this slope the over-all volume 

 change may be calculated. Similar reasoning applied to the activation 

 free energy leads to comparable expressions for the variation in the rate 

 constant with pressure: 



PAY* 



ln^=lnAo ^^ (15-110) 



h = k,-(P^v'iRT) (15-111) 



where Aq is the rate constant at zero pressure. Plots of log k against P 

 thus provide information on the volume change for the formation of the 

 activated complex. 



The variation of enzyme rate with the pressure will depend on the sub- 

 strate concentration relative to K,,^ and on whether Z„, = K, or not. 



K,n = K- 



{^) <K, ^ = ^^e-P(JF+jF2*)/iir (15-112) 



J^m ^ hl^\' 



(S) > if, V = Voe-^P''V,VRT) (15-113) 



(S)<^,„ V = v,e-<P-'V,*/RT> (15-114) 



(S) > A^„ V = Voe-^P''V,*/RT) (15-115) 



where Vq is the rate at zero pressure (or for practical pur])oses at normal 

 atmospheric pressure), W corresponds to the formation of the ES complex. 



