The daily production of acids in our body is about 60 mmol released into 6 Acid-base homeostasis is — Physical Chemistry — Thermodynamics Chemistry Question
Acid-base equilibria in blood
The daily production of acids in our body is about 60 mmol released into 6 Acid-base homeostasis is one of the most strictly regulated systems in living organisms. Blood buffers are responsible for the short-term stability of pH. The most important one is the bicarbonate buffer, the components of which are further regulated by the lungs and kidneys.
The importance of pH regulation in a narrow window can be illustrated by its influence on other physiological networks, for example, oxygen transport mediated by red blood cells containing haemoglobin. Haemoglobin has lower affinity to oxygen in tissues with a lower value of pH.
Data for calculations:
Dissociation constants of dissolved carbon dioxide: pKa (37 °C) = 6.1, pKa (25 °C) = 6.35;
Enthalpy of vaporization: ΔHvap(CO2, blood) = 19.95 kJ mol−1
Henry’s solubility of CO2 in blood at 37 °C: Hcp(CO2, 37 °C, blood) = 2.3×10−4 mol m−3 Pa−1
Consider ideal behaviour and the concentration of carbonic acid [H2CO3] = 0.
The daily production of acids in our body is about 60 mmol released into 6 dm3 of blood. For simplification, consider the blood bicarbonate buffer as a closed system initially containing only bicarbonate buffer with pH = 7.4. The partial pressure of CO2 is p(CO2) = 5.3 kPa. Calculate the pH at 37 °C, provided that the above-mentioned acidic burden is buffered by the bicarbonate buffer at physiological conditions.
Model Answer
CO2 concentration:
[CO2] = Hcp × p(CO2)
[CO2] = 2.3 × 10−7 × 5 300 mol dm−3
[CO2] = 1.219 × 10−3 mol dm−3
The initial concentration of bicarbonate in blood with no acid added, c(HCO3−, 37 °C):
log[HCO3−] = pH − pKa + log[CO2]
log[HCO3−] = 7.4 − 6.1 + log(1.219×10−3)
log[HCO3−] = 7.4 − 6.1 − 2.9
log[HCO3-] = −1.6
[HCO3−] = 24 mmol dm−3
pH after 10 mmol of acids were added to 1 dm3 of the buffer solution:
pH = 6.21
However, blood is best considered to be an open system, taking into account that the partial CO2 pressure is maintained at a constant level by respiration. Calculate the final pH for the bicarbonate buffer under the same conditions as described in task 9.1, assuming that p(CO2) does not change upon the addition of acids. Does the pH value fall into the physiologic range? Explain.
Model Answer
pH = 7.17
The buffering capacity of the bicarbonate buffer is higher when the system is open. However, pH is still outside the physiologic range (pH = 7.36–7.44). Non-bicarbonate buffers (e.g. albumin, phosphate, haemoglobin) that are present in blood additionally increase the overall buffering capacity of blood and help to keep pH within the physiologic range.
During cardiac surgery, patients are cooled down to hypothermia in order to prevent brain damage and to slow down their metabolism. Calculate pH at 20 °C (under the conditions of hypothermia), considering that p(CO2) and the concentration of bicarbonate remain unchanged.
Model Answer
The van ’t Hoff’s equation will be used:
First, the integrated form is applied to calculate the reaction enthalpy from the pKa values at 37 °C and 25 °C.
ΔrH = 36.88 kJ mol-1
Then, that same equation is used to calculate the pKa at 20 °C:
lnK293.15 = – 14.87
K293.15 = 3.48×10-7
pKa(293.15 K) = 6.46
Henry’s solubility of CO2 is recalculated in an analogous way:
Finally, the pH of blood at 20 °C is obtained using these recalculated values:
pH = 7.57
During physical activity, pH in muscles decreases due to anaerobic metabolism. In lungs, on the other hand, CO2 is removed from the bloodstream. How do these processes influence the haemoglobin-mediated oxygen transport?
Model Answer
In a working muscle, high oxygen supply is ensured by lowering the affinity towards oxygen in an acidic environment. In lungs, by contrast, CO2 is liberated from haemoglobin in red blood cells, which, in turn, binds oxygen with a greater affinity.