MECHANISMS OF ION TRANSPORT 29 



dc/dx= the concentration gradient; 



A = area of cross-section across which diffusion occurs; 

 and D = the diffusion coefficient. 



dm is expressed in gms; dc in g/cm^; dx in cm; t, in sec; and A in 

 cm^. D has the dimensions of area divided by time, and is thus 

 expressed in cm^ sec~^ 



D varies for different solutes and solvents, and is slightly affected 

 by c, by dc/dx, and by temperature. The temperature coefficient 

 (Qio) for diffusion (i.e. the rate of diffusion at one temperature 

 divided by that at a temperature 10 °C lower) is commonly about 1 -2 

 for aqueous solutions. The negative sign of /) is a convention 

 indicating that diffusion occurs from a higher to a lower con- 

 centration. Pick's law applies equally to particles of solute and 

 solvent, the only significant difference between the two, as far as 

 diffusion is concerned, being one of relative concentration. 



Salts in aqueous solution can be assigned a single diffusion 

 coefficient, even though they are dissociated into two or more ions. 

 This happens because the pairs or groups of oppositely charged 

 particles do not become perceptibly separated during diffusion owing 

 to electrical attraction; the rate of diffusion of the salt is thus 

 determined by that of the least mobile ion species. The situation is 

 different when an electrical potential gradient exists in the solution. 

 Positive and negative charges then tend to move in opposite 

 directions (electro-diffusion), in accordance with Le Chatelier's 

 principle that movement of a charged particle tends to annul the 

 applied potential difference, (cf. electro-osmosis, p. 32). 



As in all spontaneous processes where temperature remains 

 constant, and no energy is absorbed from the surroundings, diffusion 

 involves dissipation of "free energy" and the "entropy" of the 

 system increases.* Assuming that a small number of solute mole- 

 cules, m, diffuse from a large volume of solution at a concentration 

 Ci into a similar volume at a lower concentration, C2, both at the 

 same temperature, the loss in free energy in the system is given by 

 the equation : 



— A(7 = mi?nn (C1/C2) 



where R is the gas constant, and T, the absolute temperature, 



• For a clear account of the meanings of "free energy" and "entropy," see 

 Bull (1951). 



