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GASES LAWSGASES LAWS
and and
ALVEOLAR EQUATIONALVEOLAR EQUATION
DefinitionsDefinitionsF – fraction of gas in a given medium
– I: Inspiratory air– A: alveolar space
P– partial pressure of a gas in a given medium– I: Inspired air – A: alveolar space – a: pulmonary capillary
V – rate of production/movement of gas– VA: alveolar ventilation– VCO2: rate of production/elimination of CO2
– VO2: rate of production/elimination of O2
Boyle’s Law (P1Boyle’s Law (P1XXV1=P2V1=P2XXV2)V2)
As the size of closed container decreases, pressure inside is increased
The molecules have less wall area to strike so the pressure on each inch of area increases.
Charles lawCharles law
At constant temperature
2
1
2
1
TT
VV
* If temp rises gas volume increases too
For Ideal gasFor Ideal gas
TRnVP
Dalton’s LawDalton’s Law Each gas in a mixture of gases exerts its own
pressure– as if all other gases were not present– partial pressures denoted as p
Total pressure is sum of all partial pressures– Fir inspired air at atmospheric pressure (760
mm Hg) = pO2 + pCO2 + pN2 + pH2O– to determine partial pressure of O2-- multiply
760 by % of air that is O2 (21%) = 160 mm Hg
Dalton’s lawDalton’s law
In dry gas
In air saturated with water vapor
xbarx FPP
xOHbarx FPPP )(2
Dalton’s Law of Partial Dalton’s Law of Partial PressurePressure
Total Pressure = Sum of individual gas pressures.
Partial Pressure = Pressure that each gas would exert if it were alone.
What is Composition of Air?What is Composition of Air?
Oxygen – 21% or 159.6 torr
Nitrogen – 78% or 592.8 torr
Carbon dioxide - .004% or 3 torr
Water vapor – 1.25% or 8.75 torr
Alveolar GasesAlveolar Gases
Nitrogen- 74.9% or 569 torr
Oxygen- 13.7% or 104 torr
Carbon dioxide- 5.2% or 40 torr
Water vapor- 6.2% or 47 torr
Gas ExchangeGas Exchange
Earth’s atmosphere is about 78% Nitrogen and
about 21% O2
What happens to the air when we inhale?
GAS INHALED EXHALED
O2 20.71% 14.6%
CO2 .004% 4.0%
H2O 1.25% 5.9%
Gas Exchange in Lungs & Gas Exchange in Lungs & TissuesTissues
Gases in Atmosphere[%]
– N2 78.6
– O2 20.9
– CO2 0.04
– H2O 0.46
Gases in Alveoli[%]
– N2 74.9
– O2 13.7
– CO2 5.2
– H2O 6.2
Henry’s LawHenry’s Law
Quantity of a gas x that will dissolve in a liquid
Vx depends upon the solubility coefficient of the
gas in liquid and to it’s partial pressure in the
liquid-gas interface
xxx PV
Oxygen partial pressure at Oxygen partial pressure at sea levelsea level
mmHgPPFP OHatmIOIO 150)47760(21.0)(222
Production and elimination of CO2Production and elimination of CO2
AOHatm
aCOA
OHatm
ACOAACOCO V
PP
PV
PP
PVFV
2
2
2
2
22
Elimination of O2Elimination of O2
AAOAIOO VFVFV 222
AAOAIOOHatmO VPVPPPV 2222
The alveolar gas equationThe alveolar gas equation
OHatmA
OIOAO PP
V
VPP
2
2
22
Alveolar gas equationAlveolar gas equation
OHatmA
OIOAO PP
V
VPP
2
2
22
AOHatm
aCOA
OHatm
ACOAACOCO V
PP
PV
PP
PVFV
2
2
2
2
22
Alveolar gas equationAlveolar gas equation
22
2
22 aCOCO
OIOAO P
V
VPP
Alveolar gas equationAlveolar gas equation
22
2
22 aCOCO
OIOAO P
V
VPP
2
2
O
CO
V
VR
R
PPP
aCOIOAO
2
22
Alveolar gas equationAlveolar gas equation
R - Respiratory coefficientR - Respiratory coefficient
Property of Property of Gases/AtmosphereGases/Atmosphere
Increasing altitude - reduced air pressure - reduced O2 levels– e.g. at 3,000 m 563 mm Hg, O2 14.5 %
– (in water descend of 10 m increased pressure by 760 mm Hg)
Water solubility of Gases (relative)– CO2:O2:N2 ca. 20:1:0 (overall decrease with rising
temperature)
– hyperbaric O2-chamber: treatment of Gangrene, asphyxiation, circulatory shock, etc.
O2 toxicity >2.5 - 3 x above normal
(A-a) O2 difference(A-a) O2 difference Clinical significance –
– Bed-side measure of gas (oxygen) transfer
Can be calculated easily from the alveolar gas
equation and from blood gases analysis
Normal values < 20 mm Hg
Different forms of Hypoxia:
– With normal (A-a) O2 difference
– With increased (A-a) O2 difference
Calculation of (A-a) O2 Calculation of (A-a) O2 differencedifference
(A-a) O 2 Difference = PAO2 – PaO2
PAO2 = PIO2 – PaCO2/R
PIO2 = (Pb – PH2O) x FIO2
PAO2 = (Pb – PH2O) x FIO2 – PaCO2/R
PaO2 & PaCO2 – Measured in ABG
