section 1.4
H+ Concentration and pH
15
Initial State
Compartment 1
Contains a solution of impermeant
anion (Protein ) and diffusible
cation (Na+)
N tf Proteins-
Concentration C,
Na+=C,
Proteins- = C,
Semipermeable membrane
Compartment 2
Contains a solution of sodium
chloride, which dissociates
into two diffusible ions
Concentration C2
Na+ = C,
c f= c ,
Since there is Cl concentration gradient, Cl migrates (along with Na+) from
2 to 1. Let this be x.
Final State
(equilibrium has been achieved)
Compartment 1
Proteins- (C,)
Na+ (C, + x)
-
N
Cl
(x)
0
n<
low
__
Compartment 2
Na+ (C ;-x)
* Cl
(Q> —
x)
FIGURE 1-13
Gibbs-Donnan equilibrium exists in systems consisting of two fluid
compartments separated by a semipermeable membrane, which permits
diffusion of some ions (e.g., Na+, Cl- ) but is impermeable to protein
anions. Note that the concentration of diffusible cation in compartment 1 is
greater than in compartment 2 and that osmotic differences exist between
compartments 1
and 2.
concentration of C
2
(Figure 1-13). For simplicity, assume
n =
1. The initial concentration of Cl- is higher in com-
partment 2 than in compartment 1 so that Cl- will diffuse
into compartment 2. Na+ also migrates into compartment
2 to maintain electrical neutrality. This net migration oc-
curs until an equilibrium is reached, i.e., when the rate of
ion diffusion from 2 into 1 equals that from 1 into 2. If
x represents the net concentration of Na+ or Cl- trans-
ferred to compartment
1
, the final equilibrium concentra-
tions differ from the initial values by ±x (Figure 1-13).
The rate of diffusion of NaCl from 2 into 1 is proportional
to the product of the concentrations of Na+ and Cl- in
2, which is (C
2
x)2. Similarly, the rate of diffusion of
NaCl from 1 into 2 is proportional to the product of the
concentrations of Na+ and Cl- in 1, which is (Ci + x)x.
At equilibrium, the diffusion rates from 2 into 1 and 1 into
2
are equal:
(Ci + x)x = (C
2
- x
) 2
From which,
Q + 2C
2
This unequal equilibrium distribution of solutes depends
upon the concentration of both the nondiffusible protein
anion Ci and the value of C2. This disparity in ion con-
centrations also causes differences in osmotic pressure.
In the above example, if H+ replaced Na+ as the dif-
fusible cation, the Gibbs-Donnan effect would lead to
a pH change; compartment 1 would have a decrease in
pH, while compartment 2 would have an increase in pH.
Consistent with this, relatively protein-rich plasma has a
higher [H+] (i.e., lower pH) than that of protein-poor in-
terstitial fluid. Although Gibbs-Donnan equilibria affect
ionic concentrations between many compartments (e.g.,
blood/interstitial fluid or plasma/red blood cells), major
ionic gradients between various compartments are main-
tained at the expense of energy-requiring transport sys-
tems (e.g., ATP-dependent Na+ and K+ transport at cell
membranes).
1.4 H+ Concentration and pH
The use of pH to designate [H+] is due to the fact that a
broad range of [H+] can be compressed within the manage-
able numerical scale of 0-14. However, in clinical acid-
base problems, use of the pH scale has some disadvan-
tages. Since the pH is the logarithm of the reciprocal of
[H+], significant variations of [H+] in a patient may not be
fully appreciated. For example, if the blood pH decreases
from 7.4 to 7.1, [H+] is doubled; or if the pH increases
from 7.4 to 7.7, [H+] is halved (Figure 1-14). In addition,
the use of the pH scale masks the relationship between
[H+] and the concentrations of other cations, e.g., Na+ and
K+. Thus, in clinical situations it is preferable to express
FIGURE 1-14
The relationship of pH to hydrogen ion concentration (in nanomoles per
liter). The normal blood pH of 7.40 corresponds to 40 nmol/L of H+. The
solid straight line is drawn to show the linear relationship between the
concentration of H+ and pH, over the pH range of 7.20-7.50. A 0.01-unit
change in pH is equivalent to about 1.0 nmol/L change in the opposite
direction.