1.1
CHARACTERISTICS OF GASES
Basics
Molecular weight
1 mole of a substance (atoms, ions, molecules, or formula units) is
defined as the molecular weight of the substance in grams, e.g. 1 mole of
2
oxygen (O , molecular weight 32), weighs 32 grams.
Avogadro’s number
Avogadro’s number (6.022 x 1023) is approximately the number of
particles (atoms, ions, molecules, or formula units) contained in 1 mole of a
15
D. Mathieu (ed.), Handbook on Hyperbaric Medicine, 15–23.
© 2006 Springer. Printed in the Netherlands.
W. Welslau 16
substance. In German-speaking countries this constant is also known as
Loschmidt’snumber.
Avogadro’s law
Avogadro’s law states that equal volumes of gases, at the same
temperature and pressure, contain equal numbers of molecules. At standard
conditions (0°C, 1.013bar) the volume of any gas is 22.42 l/mol.
1.2 Pressure
Pressure is the application of force to a surface, and the concentration of
that force on a given area. A finger can be pressed against a wall without
making any lasting impression; however, the same finger pushing a
thumbtack can easily damage the wall, even though the applied force is the
same, because the point concentrates that force on a smaller area. More
formally, pressure (symbol: p or P) is the measure of the normal component
of force that acts on a unit area.
Table1.1-1. Pressure units
1 Pa Pascal (SI unit) = 1 Newton/m² (= N/m²)
1 kPa Kilopascal (SI unit) = 1,000 N/m²
1 MPa Megapascal (SI unit) = 1,000,000 N/m²
1 bar bar (accepted by SI) =
100,000
100
0.1
750.06
14.5
Pa
kPa
MPa
mm Hg
psi
1 atm
1 ata
physical atmosphere
atmospheres absolute
1.013 760 1.033 14.696 10.08 33.07 33.90
bar
mm Hg
kp/cm² (= at)
psi
metres sea water
feet sea water (= fsw)
feet fresh water
1 mm Hg millimetres of mercury = 133.32 Pa
1 psi
1 psig
pounds per square inch
psi gauge pressure = 0.069 bar
In the literature different pressure units are mentioned even though there
have been international agreements regarding standardized nomenclature for
many years. Following this international standardization (SI) the units
‘Pascal’ [Pa], ‘Kilopascal’ [kPa] or ‘Megapascal’ [MPa] should be used (SI
units), and the unit ‘Bar’ [bar] is accepted. Nevertheless in hyperbaric
medicine you still will find old units (ata)or imperial units (psi, fsw). In
many countries, mm Hg is still used for blood pressure and blood gases.
1.1. Physics of Hyperbaric Pressure
1.3
Density
Density (symbol:
17
= Greek letter ‘rho’) is a measure of mass per unit of
volume. The higher an object’s density, the higher is its mass per volume.
The average density of an object equals its total mass divided by its total
volume.
Practical relevance: Gas density (in addition to viscosity) is an important
factor in the resistance to breathing different inspired gases.
Table 1.1-2. Density of different gases and air
Gas
Density at 0 °C and 101.3kPa [kg/m³]
helium (He)
nitrogen (N2)
carbon dioxide (CO2)
oxygen (O2)
air (mixed gas)
0.17868
1.25060
1.97690
1.42895
1.29300
1.4
Air
Atmospheric air is a gaseous mixture consisting of different gases (see
table below). In hyperbaric practice it is accurate enough to speak of air as a
mixture of ~ 21% oxygen + ~ 79% nitrogen (including ~ 1% of the noble gas
argon, which behaves similarly to nitrogen). The fraction of CO2 is
negligible. CO2 is only important in expired gas, where the CO2 fraction at
atmospheric (= normobaric) pressure is ~ 4%.
Table 1.1-3. Components of air
Gas
Vol. % in air
nitrogen (N2)
oxygen (O2)
carbon dioxide (CO2)
argon (Ar)
neon (Ne)
helium (He)
krypton (Kr)
hydrogen (H2)
xenon (Xe)
ozone (O3)
water vapour (H2O)
78.1
20.93
0.038 (see above)
0.93
0.0018
0.00053
0.00011
0.00005
0.000008
0.000002
(see below)
Water vapour is a very variable component of air. At higher temperatures
air may contain higher amounts of water vapour. The unit ‘% of relative
humidity’ is temperature dependent. Like all other gases in the air mixture
water vapour produces a gas pressure (pH2O). At 37°C and 100% of relative
humidity (= 100% saturation with water vapour) pH2O equals 47 mmHg.
18
1.4.1
W. Welslau
Oxygen
Discovered by Joseph Priestley in 1774, oxygen at ambient temperature
and pressure is a colourless, odourless and tasteless gas. It consists of a
diatomic molecule with the chemical formula O2, and molecular weight 32.
Oxygen is a major component of air and is necessary for aerobic respiration.
It
is the second largest single component of the Earth’s atmosphere
(20.947% by volume). Due to its electronegativity, oxygen forms chemical
bonds with almost all other elements (which is the original definition of
oxidation). The only elements to escape the possibility of oxidation are a few
of the noble gases. The most famous of these oxides is dihydrogen oxide, or
water (H2O). Oxygen promotes fire. For more details see later chapters.
1.4.2
Nitrogen
Discovered by Daniel Rutherford in 1772, nitrogen at ambient
temperature and pressure is a colourless, odourless, tasteless and mostly
unreactive (ie inert) diatomic non-metal gas. It consists of a diatomic
molecule with the chemical formula N2, and molecular weight 28. Nitrogen
is the largest single component of the Earth’s atmosphere (78.084% by
volume). Nitrogen is nearly insoluble in water, which is important for bubble
formation in supersaturated tissues in decompression sickness.
1.4.3
Carbon dioxide
First described by Baptist van Helmont in the 17th century, carbon
dioxide at ambient temperature and pressure is a colourless, odourless and
tasteless gas, with molecular weight 44. CO2 is a chemical compound with
two double bounds (O=C=O). As it is fully oxidized, it is not very reactive
and particularly inflammable. CO2 is very soluble in water (0.145g CO2 in
100g H2O). When dissolved in water, about 1% of CO2 turns into carbonic
acid, which in turn dissociates partly to form bicarbonate and carbonate ions.
In 2004, the worldwide atmospheric concentration of CO2 was 0.038 %.

2.1
GAS LAWS
Boyle’s Law
First described independently by Sir Robert Boyle (1627-1691) and
Edme Mariotte (1620–1684), it is also called the ‘Boyle-Mariotte Law’:
1.1. Physics of Hyperbaric Pressure
19
‘The product of pressure (p) and volume (V) in a confined amount of gas
at equal temperature (T) remains constant.’
p
V
const
.
for
T
const
.
For a confined amount of gas in two different states, we can say:
p
1
V
1
p
2
V
2
for
T
const
.
where: 1 = state 1 of confined amount of gas
2= state 2 of confined amount of gas
Figure 1.1-1. Principle of Boyle’s law (Welslau, 2004)
Practical relevance: Inside hyperbaric chambers any confined gas volume
in the human body and in (medical) equipment is subject to this law. In gas
filled spaces with rigid walls, this effect has to be accommodated during
compression to and decompression from higher pressures. This is most
important between 1bar and 1.5bar (100kPa – 150kPa) where changes of
pressure cause the biggest relative changes of volume.
2.2
Amontons’ law
Discovered by Guillaume Amontons (1663-1705) and published in detail
by Thomas Graham (1805–1869), it is also called ‘Graham’s Law’. In
simple words, it states:
‘The quotient of pressure (p) and temperature (T) in a confined amount
of gas at equal volume (V) remains constant.’
W. Welslau 20
. . const V for const T
p or
2
2
1
1
T
p
T
p
In the above formula, temperature is to be expressed in Kelvin[K]. The
Kelvin scale starts at the lowest conceivable temperature (0K = -273°C) and
has the same graduation as the Celsius centigrade scale. For conversion from
Celsius centigrade [°C] to Kelvin [°K] you just have to add +273 (ie 273°K
= 0°C, or 373° K = 100°C).
Practical relevance: During (rapid) compression the compressed gas
inside a hyperbaric chamber warms up (see below under adiabatic
compression). When the target pressure is reached and all valves have been
closed, the compressed gas is slowly cooled down to ambient temperature by
temperature exchange through the chamber wall. According to Amontons’
Law, this is accompanied by a drop in pressure, for which a correction must
be made in order to keep the pressure at therapeutic levels.
2.3 Ideal Gas Law
Besides the gas laws of Boyle and Amontons, there are a few more which
unfortunately we can not explain here. However, in order to understand the
principal relationship between temperature, pressure and volume of gases it
is adequate to put the two explained laws together and build a simplified
equation of theIdeal Gas Law, also known as Universal Gas Equation.
. const T
V p or
2
2 2
1
1 1
T
V p
T
V p
2.4 Dalton’s Law
First described by John Dalton (1766–1844) in 1801, this gas law is also
called ‘Dalton’s law of partial pressure’. It states that:
‘The total pressure exerted by a gaseous mixture is equal to the sum of
the pressures that would be exerted by the gases if they alone were
present and occupied the total volume.’
n tot
p p p P … 2 1
where: p1, p2, … pn represent the partial pressures of each component.
1.1. Physics of Hyperbaric Pressure
21
Each gas in a mixture acts as if the other gas was not present, the pressures
that come from each gas can simply be added. Dalton’s law allows
calculating the partial pressure of each gas as follows:
‘The partial pressure of a gas (p1) equals the product of total pressure of
the gaseous mixture (Ptot) and the fraction of the gas (F1)’
p
1
P
tot
F
1
where: Fraction (F) is defined as a part of 1; i. e. in air F
O2 is 0.21.
Practical relevance: Gases which are non toxic when inhaled at ambient
pressure in a certain percentage of a gaseous mixture (Vol. %) may become
toxic when inhaled at elevated total pressure because the partial pressure,
and not the percentage in a gaseous mixture, causes toxicity.
2.5
Henry’s Law
First formulated by William Henry (1775-1836) in 1803 this law states:
‘The mass of a gas (C) that dissolves in a defined volume of liquid is
directly proportional to the pressure of the gas (P) (provided the gas
does not react with the solvent)’.
C
p
const
.
for
T
const
.
where: p = partial pressure of the gas above the liquid
C = concentration of the gas in the liquid
= Bunsen’s solubility coefficient (specific for gases and liquids)
Figure 1.1-2. Principle of Henry’s gas law (Welslau, 2004)
W. Welslau 22
The solubility coefficient for gases in liquids [millilitres of
gas/atm/litre of fluid] described by Robert Wilhelm Bunsen (1811–1899)
may also be expressed as Henry’s law constant (k). As a basic principle, the
solubility of gases is greater in cold liquids.
Table 1.1-4. Bunsen’s solubility coefficient for different gases in water
Temp. [°C] Air Oxygen Nitrogen Helium Carbon dioxide
0 29.2 48.9 23.5 9.5 35.4
5 25.7 42.9 20.9 9.2 31.5
10 22.8 38.0 18.6 9.0 28.2
15 20.6 34.2 16.9 8.8 25.4
20 18.7 31.0 15.5 8.7 23.2
25 17.1 28.3 14.3 8.5 21.4
30 15.6 26.1 13.4 8.4 20.0
35 14.8 24.4 12.6 8.3 18.8
40 14.1 23.1 11.8 8.3 17.6
Practical relevance: The pressure dependent solubility of inert gases (e.g.
nitrogen) in body liquids and tissues is crucial for the development of
decompression sickness (DCS) due to supersaturation of tissues in relation to
reduced ambient pressure after exposure.
2.6 Gas diffusion
Fick’s Laws of Diffusion were derived by Adolf Fick in 1858. Fick’s
First Law is used in steady state diffusion. This law gives rise to the formula
below, which states the rate of diffusion of a gas across a membrane.
D
P A K diffusion of Rate
where:
K = constant (determined by experiment, gas and temperature specific)
A = surface area over which diffusion is taking place
P= difference of gas partial pressure on both sides of the membrane
D = distance over which diffusion takes place, ie membrane thickness
Practical relevance: At various places in the human body partial
pressures (or concentrations) of dissolved gases, such as oxygen or nitrogen,
depend on diffusion. According to Fick’s First Law of Diffusion we can
identify the variables for diffusion of gases as size of diffusion area,
thickness of diffusion barrier (or distance), and differential gas partial
pressure. According to Fick’s Second Law of Diffusion, the time needed for
diffusion is dependent on size of molecules, allowing smaller gas molecules
like helium to diffuse faster than larger ones.
1.1. Physics of Hyperbaric Pressure
2.7
Adiabatic processes
23
Adiabatic processes happen without external heating or cooling. In
Hyperbaric Medicine, the Joule-Thomson effect and adiabatic compression
are of interest.
Joule-Thomson effect
‘When letting a gas expand adiabatically (= without external heating),
the gas will cool down.’
The Joule-Thomson effect was first described by James Prescott Joule
(1818-1889) and Sir William Thomson (1824–1907). During adiabatic
decompression, most gases at atmospheric pressure behave like this, the only
gas which warms upon expansion under standard conditions being hydrogen.
Adiabatic compression
‘When compressing a gas adiabatically (ie without external cooling), the
gas will warm up.’
Adiabatic compression describes the opposite effect.
Practical relevance: During compression, the gas inside a hyperbaric
chamber warms up. The faster the compression, the more the compressed
gas will warm up. Compression of a hyperbaric chamber for treatment of
DCS to 280kPa “as fast as possible” (e.g., according to US Navy treatment
table 6) may lead to a temperature of 40°C or more. Rapid decompression
has the opposite effect.