Gas laws
To understand the processes involved in respiration and how valid
measurements are made, it is important to understand the behaviour of gases in
both gas mixtures and liquids.
Fractional concentration and partial pressure of gases in a gas mixture
Dalton’s law states that when two or more gases, which do not
react chemically, are present in the same container, the total pressure is the
sum of the partial pressures (the pressure that each gas would exert if
isolated in the container).
The total pressure exerted by the atmosphere was traditionally measured
by inverting a long mercury fille glass tube over a mercury reservoir. At sea
level, the height of the column supported is normally about 760 mm, so barometric pressure is 760 mmHg (1 mmHg ∼=
1 torr), which in SI units is about
101 kPa (1 kPa = 7.50 mmHg). Dried air
contains approximately 21% oxygen (i.e. oxygen fraction (F02)
0.21). The remaining gases are nitrogen, 78.1%, and inert gases such as argon
and helium, 0.9%, although for convenience these physiologically inert gases
are often pooled as 'nitrogen, 79%'. Air is considered to be C02-free,
as the amount present (0.04%) is very small. According to Dalton's law:
Dry partial pressure oxygen in inspired air ( PI02 )
= oxygen fraction (F02 ) × total barometric pressure ( PB)
= 0.21 × 101 (760) = 21.2 kPa (159 mmHg)
At altitude, the oxygen fraction of air is unaltered, but
barometric pressure is reduced, being about 33.6 kPa (252 mmHg) on the top of
Everest (Fig. 4a).
Water vapour pressure
Air contains variable amounts of water vapour, depending on the water it
has been exposed to and the temperature. The maximum or saturated water
vapour pressure is higher in warm than in cool air: at 20◦C, it is 2.33 kPa (17.5 mmHg), whereas at body
temperature (37◦C), it is 6.3 kPa (47
mmHg). The relative humidity (actual/saturated water vapour pressure ×
100%) of inspired air varies with the weather; if it is 40% at 20◦C, water
vapour pressure will be 0.9 kPa (7 mmHg). The presence of water vapour means that
ambient Fo2 and Fn2 are usually a little
lower than the dry fractions given above. Air passing down the airways quickly
reaches body temperature (37◦C) and 100% saturation. Total pressure remains
close to barometric, so the added water vapour causes significan dilution of
the other gases. The available pressure for the other gases is therefore Pb
−6.3 kPa (Pb −47 mmHg).
The partial pressure of moist inspired oxygen (P ( PB
− saturated vapour pressure at 37◦C) IO2 ) = 0.21× Moistened inspired Pio2 is always 1.3 kPa
(= 0.21 × 6.1) or 10 mmHg less than dry Po2. Note that this
has a proportionally greater effect on Pio2 at high altitude
than at sea level. If dry air is saturated with water at 37◦C, at sea level Pio2
falls by 6% from 21.2 to 19.9 kPa (159-149 mmHg); on the summit of Everest, Pio2
falls from 7.0 to 5.7 kPa (52-42 mmHg), a 19% reduction.
The effect of pressure and temperature on gas volumes
The inverse relationship between the volume of a perfect gas and its
pressure, described by Boyle’s law (P ∝ 1/V), and the direct relationship
between volume and absolute temperature ( 273 ◦C), described by Charles’ law
(V T), are important when measuring gas volumes. Expired gas collected in a
bag or spirometer will shrink, both because of the direct effect of falling
temperature (Charles' law) and because water vapour condenses as temperature
falls. To enable valid comparisons, volumes at ambient temperature and
pressure saturated with water (ATPS) are corrected to those they would
occupy under standard conditions. For measurements of lung volumes, this is to body
temperature and pressure saturated with water (BTPS).
For 02 consumption or C02 production, standard
temperature and pressure dry (STPD) (0◦C, 101.3 kPa (760 mmHg), Ph2o
0) are usually used, so that each litre contains the same number of molecules (1 mole 22.4 L). Boyle's law, Charles' law and the reduction of saturated vapour
pressure with temperature are combined in the equations for correcting volumes
given in Fig. 4b.
Gases dissolved in liquids
If a gas is exposed to a liquid to which it does not react, gas particles
will move into the liquid. Henry’s law states that the number of
molecules dissolving in the liquid is directly proportional to the partial
pressure at the surface of the gas.
The constant of proportionality is the solubility of the gas in the
liquid, and it is affected by the gas, the liquid and the temperature, tending
to fall as temperature rises.
Content of dissolved gas X in a liquid Y solubility of X in Y partial
pressure of X at surface The partial
pressure of a gas in a liquid or gas tension is a more diff cult
concept than that of partial pressure in a gas phase, where we can visualize
the pressure of the molecules holding up a column of mercury. The molecules of
the gas in the liquid phase will move about in the liquid and have a tendency
to escape from the surface, which can be opposed by molecules of the same gas
in a gas phase in contact with the liquid (Fig. 4c). If the partial pressure of
the gas in the gas phase is altered until there is no net movement of gas
between the gas phase and the liquid phase, the gas and liquid are said to be
in equilibrium. By definition the partial pressure of a gas in a liquid is
equal to the partial pressure of that gas in a gas phase with which it is in
equilibrium. Partial pressure gradient (not concentration gradient) always determines the direction of
movement between phases such as a gas and liquid phase.
Note on time derivative symbols
Standard symbols used in respiratory physiology are given in Units and
Symbols on page 7. Time derivatives are properly denoted by a dot over the
symbol (e.g. V A, alveolar ventilation in L/min, see Units and Symbols on page
7). However, for terms such as the ventilation-perfusion ratio (V /Q) the dots
are often omitted, and this convention is followed ghout this book.
