INTERPRETATION OF CARBON DIOXIDE CURVES 923 



and equation (27.16) is reduced to: 



P 2i:aAoA;* +k.i + K^kACO,] 

 n 



(27.21) - = — 2^^ 



'kJ^Jc* -\-kd + KJzd[C02]\ _ AoA;rfA;*[C02] 

 ,' 2^ / 



(which contains, as expected, only the equilibrium constant, K^, instead of 

 the velocity constants k^ and Ic'j. The half-saturating concentration is: 



1 / K,A,k*\ 



(27.22) 



and the initial slope: 



(27.23) (dP/d[C02])<> = nKMk*kd/{K^k^k* + kd) 



The limiting slanting line (roof") is: 



(27.24) Piim. = nkd[COi] 



— an expression obviously representing the maximum possible supply of 

 carbon dioxide by diffusion (multiplied by n) . 



The initial slope of the particular carbon dioxide curve, which, without 

 the diffusion limitation, would have started with the slope equal to that of 

 the limiting line (equation 27.24), i. e., according to equation 27.11, the 

 curve corresponding to /r* = ka/K^Ao, is reduced, by slow diffusion, to 

 one half its former value : 



(27.25) {dP/d[C02])o = nkd/2 



More generally, a primary curve wdth an initial slope aka is reduced by the 

 diffusion limitation to an initial slope of : 



(27-26) {dm]). = (^) "'^ 



Thus, primary curves with initial slopes between 10 and 100 ka, will 

 be confined, in consequence of slow diffusion, between ^%\ka and ^^%Q\kd, 

 i. e., their initial parts will practically coincide with the limiting straight 

 line, and thus present a picture of the "Blackman type." On the other 

 hand, primary curves that would have exceeded the limiting rate only by 

 factor of the order of unity, as well as those that would have merely ap- 

 proached, but never exceeded, this limit, will retain their individuality and 

 nonlinear shape, and will show a gradual transition from the "Blackman 

 type" to the "Bose type." A certain depressing effect of diffusion will be 

 felt even in a curve the original slope of which was as low as 0. 1 ka- (The 



