RENAL AND ACID-BASE PHYSIOLOGY 165
Case 29
Essential Calculations in Acid-Base Physiology
This case will guide you through essential calculations in acid-base physiology. Use the values provided in Table 4-2 to answer the questions.
TABLE 4-2
Coostants for Case 29
pK of HCO3-/CO2 6.1
[COxi
Pc0 2 x
0.03
QUESTIONS
1. If the EV concentration of a blood sample is 40 x 10 -9 Eq/L, what is the pH of the blood?
2. A weak acid, HA, dissociates in solution into El + and the conjugate base, A-. If the pK of this
weak acid is 4.5, will the concentration of HA or A- be higher at a pH of 7.4? How much higher
will it be?
3. For the three sets of information shown in Table 4-3, calculate the missing values.
TABLE 4-3
Acid-Base Values for Case 29
PH
A
B
7.6
C
7.2
HCO3-
P CO,
14 mEq/L
36 mm Hg
48 mm Hg
26 mEq/L
4. A man with chronic obstructive pulmonary disease is hypoventilating. The hypoventilation
caused him to retain CO2 and to increase his arterial Pco, to 70 mm Hg (much higher than the
normal value of 40 mm Hg). If his arterial HCO3 concentration is normal (24 mEq/L), what is
his arterial pH? Is this value compatible with life? What value of arterial HCO 3 would make his
arterial pH 7.4?
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PHYSIOLOGY CASES AND PROBLEMS
5. Figure 4-2 shows a titration curve for a hypothetical buffer, a weak add.
HA
3
A
i
3
4
5
I
7
6
8
9
10
PH
Figure 4-2 Titration curve for a weak add.
conjugate base.
HA,
weak acid; A-,
What is the approximate pK of this buffer? At a pH of 7.4, which is the predominant form of
the buffer, HA or A-? If 1-11- was added to a solution containing this buffer, would the greatest
change in pH occur between pH 8 and 9, between pH 6 and 7, or between pH 5 and 6?
168 PHYSIOLOGY CASES AND PROBLEMS
ANSWERS AND EXPLANATIONS
1. The pH of a solution is -log io of the IA + concentration:
pH = -log. 1111
Thus, the pH of a blood sample with an 11+ concentration of 40 x 10-9 Eq/L is:
pH = -log i o 40 x 10-9 Eq/L
= -logio 4 x 10- 8 Eq/L
= -loglo (4) + -log io (10-8)
= -0.6 + (-)(-8)
= -0.6 + 8
= 7.4
In performing this basic calculation, you were reminded that: (1) a logarithmic term is more
than a "button on my calculator"; (2) a blood pH of 7.4 (the normal value) corresponds to an
H+ concentration of 40 x 10-9 Eq/L; and (3) the H* concentration of blood is very low!
2. The Henderson-Hasselbalch equation is used to calculate the pH of a buffered solution when
the concentrations of the weak acid (HA) and the conjugate base (A-) are known. Or, it can be
used to calculate the relative concentrations of HA and A- if the pH is known.
A
pH = pK + log —
HA
where
pH = -log i n [H+]
pK =
of the equilibrium constant
A- = concentration of the conjugate base, the proton acceptor
HA = concentration of the weak acid, the proton donor
For this question, you were given the pK of a buffer (4.5) and the pH of a solution containing
this buffer (7.4), and you were asked to calculate the relative concentrations of A- and HA.
pH = pK + log
7.4 = 4.5 + log
A
HA
A
HA
2.9 = logA
HA
Taking the antilog of both sides of the equation:
794 = A-/HA
Thus, at pH 7.4, for a weak acid with a pK of 4.5, much more of the A- form than the HA form
is present (794 times more).
3. These questions concern calculations with the HCO 3-/CO2 buffer pair, which has a pK of 6.1.
For this buffer, HCO3 is the conjugate base (A-) and CO 2 is the weak acid (HA). The HendersonHasselbalch equation, as applied to the HCO 3-/CO2 buffer, is written as follows:
pH = 6.1 + log HcC03
0
RENAL, AND ACID-BASE PHYSIOLOGY 169
Although values for CO 2 are usually reported as Pc 02, for this calculation we need to know the
CO2 concentration. The CO2 concentration is calculated as Pco, x 0.03. (The conversion factor,
0.03, converts Pco, in mm Hg to CO 2 concentration in mmol/L.)
3
Pco, x 0.03
pH = 6.1 + log HCO
where
pli= -logio of [H1
6.1 = pK of the HCO 3-/CO2 buffer
HCO3 = HCO 3- concentration (mmol/L or mEq/L)
Pco, = partial pressure of CO2 (mm Hg)
0.03 = factor that converts Pco, to CO 2 concentration in blood (mmol/L per mm Hg)
14
A. pH = 6.1 + log 36 x 0.03
= 6.1 + log 12.96
= 6.1 + 1.11
= 7.21
3B. 7.6 = 6.1 + log HCO
48 x 0.03
37.6 = 6.1 + log HCO
1.44
31.5 = log HCO
1.44
Taking the antilog of both sides:
331.62 = HCO
1.44
HCO 3- = 45.5 mEq/L
C.
7.2 = 6.1 + log
1.10 = log
26
Pco, x 0.03
26
Pco, x 0.03
Taking the antilog of both sides:
12.6
26
Pco, x 0.03
Pc02 x 0.03 = 26
12.6
Pco, x 0.03 = 2.06
PCO2
= 69 mm Hg
170 PHYSIOLOGY CASES AND PROBLEMS
4.
For this question, we were given a Pco, of 70 mm Hg and an HCO 3- concentration of
24 mEq/L. We apply the Henderson-Hasselbalch equation to calculate the pH.
3
pH = 6.1 + log HCO
Pco, x 0.03
= 6.1 + log 24
70 x 0.03
= 6.1 + log 11.4
= 6.1 + 1.06
= 7.16
The lowest arterial pH that is compatible with life is 6.8. Technically, this calculated pH of 7.16
is compatible with life, but it represents severe acidemia (acidic pH of the blood). To make the
person's pH normal (7.4), his blood HCO3 concentration would have to be:
/7.4 = 6.1 + log HCO
70 x 0.03
= 6.1 + log HCO3
2.1
1.3 – log HCO
2.1
3-
Taking the antilog of both sides:
19.95 –
HCO3
2.1
HCO3- = 41.9 mEq/L
This calculation is not just an algebraic exercise; it illustrates the concept of "compensation,"
which is applied in several cases in this chapter. In acid–base balance, compensation refers to
processes that help correct the pH toward normal. This exercise with the Henderson-Hasselbalch
equation shows how a normal pH can be achieved in a person with an abnormally high Pc02.
(A normal pH can be achieved if the HCO3 concentration is increased proportionately as much
as the Pa), is increased.) Note, however, that in real-life situations, compensatory mechanisms
may restore the pH nearly (but never perfectly) to 7.4.
5. Titration curves are useful visual aids for understanding buffering and the Henderson-Hasselbalch
equation. The pK of the buffer shown in Figure 4-2 is the pH at which the concentrations of
the HA and the A- forms are equal (i.e., pH = 6.5). This pH coincides with the midpoint of the
linear range of the titration curve, where addition or removal of 1-1' causes the smallest change
in pH of the solution. To determine which form of the buffer predominates at pH 7.4, locate
pH 7.4 on the x-axis; visually, you can see that the predominant form at this pH is A-. If H + were
added to a solution containing this buffer, the greatest change in pH (of the stated choices)
would occur between pH 8 and 9.
RENAL AND ACID-BASE PHYSIOLOGY
Key topics
Buffers
Conjugate base
FICO 3-/CO 2 buffer
Henderson-Hasselbalch equation
pH
pK
Titration curve
Weak acid
171