ACID-BASE PRINCIPLES: II

Bicarbonate/C0₂ System

Buffering by bicarbonate/C0₂ comprises hydration of dissolved C0₂ ( [C0₂]_d ) and dissociation of carbonic acid:

                           (C0₂)_d + H₂0 <=> H₂C0₃ <=> H⁺ + HC0₃^-

The mass action equilibrium for the dissociation is:  (1)       K_d = [H⁺] x [HCO₃^-] / [H₂C0₃]

The equilibrium of the simultaneous hydration is:        (2)       K_h = [H₂C0₃ ]/([C0₂d] x [H₂0])

From (2)                        K_h x [H₂0] = K₁ (constant) and K₁ = [H₂CO₃]/[CO₂d]
and                                (3)    [H₂CO₃] = K₁ x [CO₂]_d
from Henry's Law         (4)   [CO₂]_d = a x P_CO2        a is the CO₂ solubility coefficient.
Thus                              (5)    K_d = [H⁺] x [HC0₃^-] / K₁ x a x P_CO2
Solving for [H⁺]            (6)    [H⁺]=K_dK₁ a P_CO2/[HCO₃^-]

Since K_dK₁a = 24       (7)   [H⁺](in nM)= 24 P_CO2(in mmHg) / HCO₃^- (in mM)   (Henderson's equation)

Taking the negative log on both sides

                                      (8)  -log [H⁺]=-log K_dK₁+log[HC0₃]/aPC0₂

Calling -log K_dK₁ = pKe (effective pK)
                                     (9)   pH = pKe + log [HCO₃^-]/aP_CO2    (Henderson-Hasselbalch equation)
      where
                              pKe = 6.1; a = 0.0301; [HCO₃^-] in mM; P_CO2 in torr (or mmHg).

Buffering by the HC03^-/CO2 system

In spite of its pKe = 6.1 the HCO3^-/CO₂ system functions as an effective buffer in maintaining the normal arterial blood plasma pH at 7.4 because one of its component is volatile and the system is open.   Consider the following example:

The ECF contains 24 mM NaHCO₃ and is equilibrated with 5.6% gaseous CO₂.  At 37C and P_B = 760 torr,
P_CO2 = 0.056 x (760-47) = 40 torr,  aP_CO2 = .0301 x 40 = 1.2 mM and [HCO₃^-]/ aP_CO2 = 24/1.2 = 20/1;
Log [HCO₃^-]/aP_CO2 = Log 20/1 = 1.3;   pH = 6.1 + 1.3 = 7.4 or [H⁺]= 24 x 40/24 = 40 nM

Buffering of strong acid in a closed system.  If we had 1 L of such a bicarbonate-CO₂ solution in a closed container and added enough strong acid (e.g. 12 mmoles HCl) to decrease the [HCO₃-] to about half (to 12 mM)  by the reaction  HCl + NaHCO₃ <=> H₂CO₃ + NaCl, then twelve mmoles of H₂C0₃ (really of H₂C0₃+C0₂d) will be now present. Thus

[HC03]= 12; aP_CO2 = 12; P_CO2 =12/0.03= 400 torr and [HCO3^-]/aP_CO2 = 1.0 ; log 1 = 0; pH = 6.1 + 0 = 6.1 and
[H⁺]= 24x400/12 =800 nM; which represents a severe acidosis.

Buffering of strong acid in an open system. Suppose the container with NaHC0₃ solution is open to the atmosphere and we bubble continuously 5.6% C0₂ to maintain the P_CO2 at 40 torr. Addition of 12 mmoles of HCl will reduce [HC0₃^-] to 12 mM but the generated H₂C0₃ will escape to the atmosphere by conversion to gaseous CO₂ because the P_CO2 is maintained at 40 torr.

[HC0₃] = 12 mM; aPC0₂ = 1.2 mM; [HCO₃^- ]/aPCO₂= 10; log 10 = 1; pH = 6.1 + 1 = 7.1; [H⁺] = 24 x 40/12 = 80 nM

Conclusion:  The resulting pH change is much smaller in an open system than in a closed system. For a buffer pair in which the weak acid is volatile, buffering of the pH upon addition of protons to an open system is very effective. In addition for such a buffer system the effective buffering range is wider (>1 pH unit above their pK) than for non volatile buffers or than for closed systems.

Buffering of strong acid in an open and regulated system. Alveolar ventilation (V_A) is under neural control.   Increases in V_A in response to reduced pH_a lead to increased pulmonary excretion of C0₂ and lowering of the P_aC02 . We can simulate this response by additional bubbling of air through the solution (simulating hyperventilation); the PC0₂ will be lower than normal (e.g. 20 torr), so

[HCO₃^-] = 12; aP_CO2 = 0.03 x 20 = 0.6; [HCO₃-]/aP_CO2 = 20; log 20 = 1.3; pH = 6.1+1.3 = 7.4; [H⁺]=24 x 20/12 = 40nM

Thus, in an open system with perfect "physiological" control, the pH change  due to addition of strong acid is completely blunted. In real life, for each 1 mM decrease in [HCO₃^-] due to acid loading, the P_aCO2 should fall by about 1 torr if the respiratory centers respond normally to the low pH_a. Usually the compensation is not perfect, some acidosis persists, and is limited by loss of bicarbonate in the urine due to the low P_aCO2 (see later).

Base Excess and Base Deficit

Titration of body fluids with CO₂. When the P_CO2 of a pure NaHCO₃ solution is elevated, the pH will decrease with little change in the [HCO₃]. Upon increasing the P_CO2, both the [CO₂]_d and the [H₂C0₃] will increase and some of the H₂C0₃ will dissociate into H⁺ (responsible for the decrease in pH) and HC03^-, the increase [HC03^-], as that in [H⁺], is in the nanomolar (10^-9M) range. When the P_CO2 of blood is similarly raised, the decrease in pH will be smaller (since blood contains buffers) and the increase in [HCO₃^-] will be larger than observed in a pure NaHC0₃ solution.This buffering of CO₂ is due to the presence of non-bicarbonate buffers in blood and tissues (mostly Hb, other proteins, and phosphates). Non-bicarbonate buffers associate with H⁺ derived from H₂C0₃, promote formation of H₂C0₃ (by hydration of C0₂) and dissociation of H₂C0₃ into H⁺ ions (which are buffered by these substances) and more HC0₃^-, which increases in concentration.

The changes in pH and [HC0₃] in arterial blood in vivo upon chronic exposure to changes in P_aC02 (chronic hypoventilation or C0₂ inhalation or chronic hyperventilation) differ from those in the acute situation. Chronic exposure to a high P_aC02  results in much smaller changes in pH_a and much larger increases in plasma [HC0₃-] than on acute exposure to the same P_aC02. This higher chronic buffering capacity for C0₂  is due to the kidneys' generation of HC0₃^-, whose ECF concentration increases and minimizes the drop in pH due to increased PC0₂.  Such "chronic" buffering of  C0₂ is 10 times larger  than the acute buffering by non-bicarbonate buffers
.
The base excess (BE) or base deficit (negative BE) is calculated from the change in [HCO₃^-] that persists in the system when the pH is brought back (by acutely changing the PCO₂) to the standard value of 7.4. At that pH, all non-bicarbonate ECF buffers (proteins, phosphates, etc.) have the same ratio of dissociated to undissociated buffer forms as existed before addition of acid or base. The base (positive values) or acid (negative values) excess is thus reflected only by the change in Standard Bicarbonate, [HCO₃^-]_St ,and is calculated as follows: 

BE = Change in [HC0₃-]_St = ([HCO₃^- ]_x - 24) + BC x (pH_x-7.4)

[HCO₃^-]_x and pH_x are the values measured in a blood sample and BC is the buffer capacity. As discussed above, the value of BC is not constant but depends on the elapsed time. In chronic acidosis the value of BC is very large (100 slykes)  while BC = 10slykes in acute acidosis. Unfortunately the ICF is not in chemical equilibrium with the ECF and we can only give an educated guess of what is happening intracellularly.  At the different stages, the product of the apparent volume of distribution of bicarbonate (40% of body weight in acute acidosis, 80% of body weight in chronic conditions) times the base deficit yield estimates of the amount (mEq) of bicarbonate to be replaced (or if in excess, to be removed). The initial target should be to bring the pH to a safe range (7.25-7.55, [H⁺], 28-56 nM), rather than to completely correct the disturbance.
 

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