210 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



which the cells are bathed. The inverse square root relationship occurs over 

 and over again in diffusion-controlled processes. 



In Figure 8-9 are shown the initial concentrations (milliequivalents per 

 liter) of Na + and K+ inside the cell (at / = 0), and their change toward the 

 concentrations in the plasma (dotted lines) following failure of the sodium 

 pump. 



Diffusion Coefficient D, and Permeability Constant P. 



Table 8-6 gives some representative values for the diffusion coefficient at 

 25°C in cm 2 sec -1 . The activation energy and the temperature coefficient 

 of rate of diffusion in water solutions and in fat and lipid, were given in 

 Table 8-3. 



TABLE 8-6. Some Diffusion Coefficients (D) (cm 2 sec ] ). 



Substance into Water (at 12° C) D x 10 5 



Glycerine 0.42 



MgS0 4 0.35 



KC1 1.59 



NaCl 1.09 



Sugar 0.29 



Urea 1.12 



Just as the specific rate constant of a chemical reaction can be broken 

 down into the factors upon which it depends, so also can the diffusion coef- 

 ficient be factored. Diffusion is a "jump process," in which the movement 

 of a species occurs by its being pushed from one position of rest to another 

 as the result of favorable collisions with neighbors. The distance between 

 successive positions of rest is called the jump distance, A. The activated 

 complex in this case is pictured as being an intermediate position in which 

 the jumping species is half way between rest sites and can go either way. 

 Detailed analysis shows that 



D = t\ 2 JiL e -*Ft/RT 



h 



where A is the jump distance in cm, AF* is the free energy of activation (Fig- 

 ure 8-4) for the "jumper," 7" is the absolute temperature (degrees Kelvin), 

 k is the Boltzmann constant, and h is Planck's constant. The units of D 

 are therefore cm 2 sec "'. Table 8-6 gives some values of D for different spe- 

 cies diffusing into water. 



As in the case of chemical reactions, the term k g T/h is a constant at any 

 temperature. The low diffusion constants (in molasses, in lipids, or in fats) 

 and high values (in water or alcohol) are determined by the values of X, and 



