Box Extension 23.1

Capacitance Coefficients Explain the Relative Partial Pressures of O2 and CO2 in Arterial Blood

During breathing, the extent to which the CO2 partial pressure of the respired medium changes relative to its change in O2 partial pressure tends to be sharply different between water breathers and air breathers because of a property of water and air called the capacitance coefficient (β). For any particular gas (O2 or CO2) and any particular respired medium (water or air), the capacitance coefficient is defined to be the change in total gas concentration in the respired medium per unit of change in gas partial pressure in the respired medium. Box Extension 23.1 explains by use of a figure how capacitance coefficients place constraints on animal physiology.

In air, O2 and CO2 have identical capacitance coefficients. In water, however, the capacitance coefficient for CO2 is at least 23 times that for O2. The explanation for this difference between air and water is that only the universal gas law (see Equation 22.1) needs to be considered in air, whereas gas solubilities must be considered in water. To explain more fully, in air—where only the universal gas law is relevant—O2 and CO2 simply follow the same principles (they adhere identically to the universal gas law). They thus have identical capacitance coefficients. However, in water—where gas solubilities are relevant—CO2 has a far higher capacitance coefficient than O2 because CO2 is much more soluble in water than O2 is (see page 588 in the book).

To see the implications of the capacitance coefficients of O2 and CO2, let’s assume that in the course of an animal’s metabolism, the number of moles of CO2 produced is equal to the number of moles of O2 consumed.[1] Under this assumption, as the respired medium—air or water—passes over the gas-exchange membranes of the animal, the concentration of CO2 in the air or water is raised by the same amount as the concentration of O2 is lowered.

In air, the capacitance coefficients of O2 and CO2 are identical. Therefore, because the CO2 concentration in respired air is raised during breathing by the same amount as the O2 concentration is lowered, the air’s CO2 partial pressure is raised by the same amount as its O2 partial pressure is lowered. The green line in the Figure shows this relation graphically. The blue dot marks the partial pressures of the two gases in fresh, atmospheric air (the inhaled air). The green line shows how the partial pressures of the two gases, CO2 and O2, vary jointly in the exhaled air. When an air breather lowers the O2 partial pressure of the respired air to any given extent, it raises the partial pressure of CO2 in the respired air to about the same extent.

Air breathers and water breathers: Simultaneous values for the CO2 partial pressure and O2 partial pressure in the exhaled air or water The blue dot shows values for natural fresh air and for water at equilibrium with fresh air. As air or water is subjected to gas exchange, its composition of dissolved gases shifts toward the upper left along the green line (air breathers) or black line (water breathers). The scales of partial pressure on the axes are shown in two systems of units, the SI system (kPa) and a traditional system (mm Hg). The green and black lines were calculated assuming the capacitance coefficient for CO2 to be about 30 times that for O2 in water (and equal to that for O2 in air) and assuming a respiratory quotient (ratio of CO2 production to O2 consumption) of 0.9. Atmospheric air typically contains water vapor and therefore has a partial pressure of O2 that is a bit lower than the value (159 mm Hg) in dry air. (After Scheid and Piiper 1997; see that reference for details of the graph shown.)

In water, the capacitance coefficient of CO2 is at least 23 times greater than that of O2. This means that in water, although the CO2 concentration of the respired water is raised by the same amount as the O2 concentration is lowered, the CO2 partial pressure is raised much less than the O2 partial pressure is lowered. The black line in the Figure depicts this relation graphically. An animal breathing water never raises the partial pressure of CO2 in respired water by much, even if it removes all the O2.

The orange areas in the Figure show the ranges of O2 and CO2 partial pressures in the systemic arterial blood of air- and water-breathing vertebrates. Because arterial blood is derived from blood leaving the breathing organs, the O2 and CO2 partial pressures in the blood are roughly predictable from the partial pressures in the exhaled medium and therefore fall on the green and black lines. The arterial CO2 partial pressure is typically only 0.1–0.6 kPa (1–4 mm Hg) in water breathers. It is far higher, 4.0–5.4 kPa (30–40 mm Hg), in air breathers.

References

Scheid, P., and J. Piiper. 1997. Vertebrate respiratory gas exchange. In W. H. Dantzler (ed.), Comparative Physiology, vol. 1 (Handbook of Physiology [Bethesda, MD], section 13), pp. 309–356. Oxford University Press, New York.

[1]This is a useful first approximation, although the actual relation depends on the types of foodstuffs being catabolized in the cells (see Table 7.2).

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