Fractional Concentration

It is important to understand the distinction between partial pressure of a gas and fractional concentration of a gas. Fractional concentration of a gas in a dry gas phase (F) is the percentage of total gas molecules occupiedby a particular gas excluding water vapor molecules. Fractional concentration is expressedas a decimal; for example, 21% O₂ is equivalent to an FO₂ of 0.21. In a container filled with only O₂ and water vapor, the fractional concentration of O₂ is 100% (FO₂ = 1.0), which is shown in Figure 3-1. The true concentration of O₂ would be less than 100% because some molecules in the container are H₂O rather than O₂; nevertheless, the percentage of O₂ in the dry gas phase (i.e., excluding PH₂O) is 100%.

Partial Pressure

The partial pressure of oxygen (PO₂) in Figure 3-1 could be determined by the application of Dalton’s law; the sum of the partial pressures equals the total pressure. Because there are only two gases in the container, the sum of their partial pressures must be equal to 240 mm Hg. Because PH₂O is given as 40 mm Hg, the balance of pressure must be due to O₂. Thus, in this example, the PO₂ is 200 mm Hg. The formula used to calculate the partial pressure of a gas is (see Fig. 3-1):

A similar container with an identical PH₂O and the same total pressure is shown in Figure 3-2. However, only two of the ten non–water molecules in this mixture of gases are O₂molecules. Thus, the fractional concentration of oxygen (FO₂) in this mixture is 0.2 (20% O₂). The partial pressure of O₂ in this mixture of gases can be calculated by:

Symbols

The symbol FIO₂ is used to refer to the percentage of inspired oxygen. It is customary to use capital letters as symbols to indicate gas measurements related to the lung or its function (e.g., I, inspired; E, expired; A, alveolar;T, tidal). Alveoli are the tiny air sacs within the lungs in which gas exchange with the blood takes place. Tidal refers to the movement of gas into and out of the lungs during normal (tidal) ventilation.

Lowercase symbols, on the other hand, are usually reserved for measurements made inthe blood (e.g., a, arterial; v, venous; c, capillary). A bar (—) over the symbol is used torepresent the mean or average. For example, PO₂ designates the average PO₂ in theveins. PO₂ can be measured in the pul-monary artery. In this blood vessel, all venous blood that has returned to the heart from throughout the body has been thoroughly mixed.

Composition of Atmosphericand Alveolar Air

The major gases present in dry atmospheric air with their respective partial pressures and percentages are shown in Table 3-1. It can be seen that the normal FIO₂ while breathing room air is 0.21 and that the normal PIO₂is approximately 158 mm Hg. Partial pressures shown are based on a total atmospheric pressure of 760 mm Hg present at sea level. For simplicity, Table 3-1 shows no water vapor pressure in the atmospheric air. In reality, the air that we breathe contains some water vapor pressure, and the normal partial pressure of inspired oxygen in humidified air is only approximately 148 mm Hg.

The partial pressures and percentages of these gases in alveolar air are also shown in Table 3-1. Two major processes are responsible for changing the quality of the air in the alveoli compared with inspired air: humidification and external respiration.

Body Temperature andPressure Saturated

Clinical measurements of gases are made under standardized conditions for compar-ison of values and reproducibility of results. Blood gases are measured at body temperature and pressure saturated (BTPS). The BTPS notation refers to normal standardized conditions within the body (i.e., temperature 37°C, ambient pressure, and PH₂O of 47 mm Hg).

Temperature, Pressure, and Volume

An introduction or review of gas behavior would be incomplete without some mention of the basic gas laws; in particular, the laws that describe the interdependent relationships between volume, pressure, and temperature are briefly described.

Gay-Lussac’s law states that if volume and mass remain fixed, the pressure exerted by a gas varies directly with the absolute temperature of the gas.⁷⁴ Absolute temperature is measured in Kelvin degrees and 0°Celsius is equivalent to 273°Kelvin (K). The total pressure in Figure 3-2 is 240 mm Hg, and the gas is at a temperature of 20°C (293°K). If the temperature ofthe gas increased to 38°C (311°K), which is shown in Figure 3-3, Brownian movement and kinetic energy of the gas would increase and the total pressure within the container would increase. As show in Figure 3-3, the new pressure is 255 mm Hg.

Similarly, the partial pressures of other gases within the container also increase. Partial pressure must be distinguished from fractional concentration, which would not change. The partial pressure of O₂ in Figure 3-3 can becalculated as described earlier:

The gas laws pertaining to changes involume are less important with regard to blood gases but are included here for completeness. Boyle’s law states that if absolute temperature and mass remain unchanged, volume varies inversely with pressure. Similarly, Charles’ law states that if pressure and mass are unchanged, volume varies directly with changes in absolute temperature.

Gases in Liquids

Gases dissolve freely in liquids. The particular gas may or may not react chemically with the liquid, depending on the chemical nature of each substance. Nevertheless, all gases remain in a free gaseous phase to some extent within the liquid. The dissolution of gases in liquids is a physical, not a chemical, process. Gases within liquids exert pressure in much the same manner as described in pure gaseous environments.

Henry’s law states that when a gas is exposed to a liquid, the partial pressure of the gas in the liquid phase equilibrates with the partial pressure of the gas in the gaseous phase. Thus, if O₂ in the air is exposed to blood or water, thereis an exchange of O₂ molecules between theliquid and gaseous phases until the respective partial pressures are equal. The progressive equilibration of the partial pressure of O₂ between the gaseous and the liquid phases is shown in Figure 3-4.

Change in Altitude

The barometric pressure is lower as altitude increases. Air at a high altitude still has a 21% O₂ concentration; however, the partial pressure of O₂ is much lower. The effect of high altitude on barometric pressure and PO₂ is shown in Table 3-3.

At the summit of Mount Everest, whichhas the highest altitude on earth, the PO₂ is approximately 42 mm Hg.⁷⁵ Again, the FIO₂ remains at 0.21 but the PO₂ decreases tremendously. Thus, the normal PaO₂ at a high altitude (e.g., Denver) is obviously much lower than the normal PaO₂ at sea level.

Clinical studies have shown that the major effect of an air bubble in a blood gas sample is a change in PaO₂.^{76 77 78 79} According to Henry’s law, when a blood specimen with a PaO₂ of less than 158 mm Hg is interfaced with an air bubble, the PaO₂ of the blood sample spuriously increases. This action occurs because the partial pressure of O₂ in the air at sea level is approximately 158 mm Hg. The magnitude of the increase depends partly on the duration of exposure, whereas the volume of the air bubble, although important, seems to make less difference.⁷⁷ Other factors that may determine the ultimate effect of aircontamination include the temperature of the sample and the degree of agitation (Fig. 3-5).

Furthermore, the change is greatest when the patient’s actual PaO₂ exceeds 100 mm Hg.⁷⁹ This change can be explained by the chemical relationship between O₂ and hemoglobin that is discussed in Chapter 7 under the oxyhemoglobin dissociation curve.

In certain clinical situations (e.g., in the operating room where high concentrations of inspired O₂ are often used), the initial PaO₂ of the blood sample may exceed 158 mm Hg. In this event, O₂ tends to migrate from the blood phase to the bubble and results in measurement of an erroneously low PaO₂ in the blood sample being analyzed.⁷⁶

As shown in Table 3-1, the PCO₂ inroom air is essentially zero. Thus, one would expect blood PCO₂ levels to decrease if blood were exposed to an air bubble. This effectdoes occur, but is less marked than the change in PO₂. The different blood solubility coefficients of O₂ and CO₂ probably explain thedisparity in response. Finally, the pH increases when arterial blood is exposed to an airbubble as a direct consequence of the decrease in PaCO₂.