92168.pdf

Kinetic properties 43

(2)

initial

concentrations

Equilibrium
concentrations

1

Pr- Io |

!

No^4 "" a + x I

Pr- - a 1

a- -x i

I

Na +

a-

Na*-

a- »

-b

-b

b-x

b-x

Figure 2.11 The Donnan membrane equilibrium

proportional to the product of the Na+ and CI~ ion concentrations

(strictly, activities), so that

rate of diffusion from (1) to (2) = k(a+x)x

rate of diffusion from (2) to (1) = k(b-x)^2

At equilibrium these rates of diffusion are equal - i.e.

or (a + x)x-(b-x)

, 2

X ~ •

a + 2b

At equilibrium the concentrations of diffusible ions in compartments

(1) and (2) are («+2jt) and 2(b-x), respectively, so that the excess

concentration in compartment (1) is (a-26+4*). Substituting for x,

this excess diffusible ion concentration works out to be a^2 l(a+2b).

Clearly, the results of osmotic pressure measurements on solutions

of charged colloidal particles, such as proteins, will be invalid unless

precautions are taken either to eliminate or to correct for this

Donnan effect. Working at the isoelectric pH of the protein will

eliminate the Donnan effect but will probably introduce new errors

due to coagulation of the protein. Working with a moderately large

salt concentration and a small protein concentration will make the