RES 105 applied science wk 8

Partial pressure

The pressure exerted by an individual component (gas) in a mixture

Dalton's Law of Partial Pressures

The sum of the partial pressures of a gas mixture equals the total pressure of the system: P1 + P2 + P3 … = Ptotal

Partial pressure of a gas in a mixture is proportional to

Its percentage of the mixture; it can be calculated as total pressure x fractional concentration

1 atm in mmHg (notes)

760 mmHg; the partial pressures (tensions) of all gases add up to 760 mmHg

How to calculate PO2 in room air

Multiply barometric pressure by the fraction of oxygen: 760 x 0.21 = 159.6 mmHg

Composition of room air (percent)

Oxygen 21%, nitrogen 78%, CO2 0.03%, trace gases 0.97%

Partial pressures in room air at 760 mmHg

PO2 159.6 mmHg; PN2 592.8 mmHg; PCO2 0.228 mmHg; trace gases 7.372 mmHg

Atmospheric pressure equation

Patm = PO2 + PN2 + PCO2 + P(trace gases) = 760 mmHg

Water vapor pressure and Dalton's Law

Water vapor pressure does not follow Dalton's law because it depends mainly on temperature; it 'displaces' the partial pressure of other gases

Water vapor pressure when calculating partial pressure of a gas saturated with water vapor

PH2O must be subtracted from the total pressure of the gas mixture

Partial pressure of a gas saturated at 37°C: formula

PO2 = (PB - PH2O) x FiO2

Example: PO2 in gas saturated at 37°C, PB 760, FiO2 0.21

(760 - 47) x 0.21 = 149.73 mmHg

PH2O at 37°C

47 mmHg (always, if temperature is 37°C)

Hyperbaric vs hypobaric conditions

Individual gas pressures increase in hyperbaric conditions and decrease in hypobaric conditions according to the percentage each gas occupies

Hyperbaric example: PO2 100 mmHg at 760; pressure raised to 1040 mmHg; new PO2?

100/760 = 0.132 (13.2%); 0.132 x 1040 = 137.28 mmHg

Example: 35% Gas A, 25% Gas B, 40% Gas C at 760 mmHg total

Gas A 266 mmHg; Gas B 190 mmHg; Gas C 304 mmHg

Example: Gas A 123 mmHg and Gas B 118 mmHg; total pressure and percentages

Total = 241 mmHg; Gas A = 51%; Gas B = 49%

Approach for missing values in partial pressure problems (notes)

Add what you know, then subtract from 760 mmHg to find what is missing

Henry's Law

At constant temperature and equilibrium, the amount of gas dissolved in a liquid is directly proportional to the pressure of that gas on the surface of the liquid

Henry's Law in practical terms

More pressure on the liquid's surface makes more gas dissolve (pressure 'pushes' gas into the liquid)

Limitation of Henry's Law

Only applies to gases that do not chemically react with the solvent (the liquid)

Henry's Law in the lungs

Gas moves from alveoli to blood until pressures are equal; the amount of O2 dissolved in blood is directly proportional to the PO2 at the blood surface (temperature held constant at body temp)

Henry's Law equation

V = a x Pgas

Henry's Law equation: V

Volume of dissolved gas

Henry's Law equation: a

The solubility coefficient of the gas in the given liquid

Henry's Law equation: Pgas

Partial pressure of the gas above the liquid

Solubility coefficient

The volume of a gas that will dissolve in 1 mL of a given liquid at standard pressure and a specified temperature

Solubility coefficient depends on

The solvent (liquid), temperature, and pressure; each gas has its own

Solubility coefficient of O2 in plasma at 37°C and 760 mmHg

0.023 mL/mL (slide 12; slide 25 uses 0.0244)

Solubility coefficient of CO2 in plasma at 37°C and 760 mmHg

0.510 mL/mL (slide 12; slide 25 uses 0.592)

What determines the volume of gas dissolved?

Both the solubility coefficient AND the pressure of the gas above the liquid's surface

Once dissolved, gases…

Exert a partial pressure in the liquid (e.g., O2 dissolved in plasma exerts a PO2)

O2 gradient across the AC membrane

60 mmHg (alveoli 100 mmHg; venous blood 40 mmHg)

Why do we increase FiO2 therapeutically?

To raise the patient's PaO2: it makes the pressure gradient bigger

Effect of temperature on gas solubility

High temperatures decrease solubility; low temperatures increase solubility

Pop/soda temperature example

Cold pop keeps its fizz longer than warm pop, which goes flat quickly

Why does temperature affect solubility?

Warm liquid increases kinetic activity of dissolved gas molecules, so more escape and partial pressure rises; the amount left in solution decreases

When is body temperature not the baseline (notes)

Hypothermic patients; we try to return them to baseline

Ventilators and Henry's Law (notes)

Ventilators can modify pressure

Diffusion

Movement of molecules in response to a gradient (pressure or concentration)

Why do gas molecules diffuse rapidly?

High kinetic energy; they continually collide with walls and each other and rebound elastically

Graham's Law of Diffusion

The rate of diffusion of a gas is inversely proportional to the square root of its gram molecular weight (density)

Does diffusion depend on volume differences?

No; it depends on gradients (concentration, pressure), not on volume differences

Factors that speed up diffusion (kinetic)

Anything that increases molecular activity (e.g., higher temperature)

Lighter vs heavier molecules (Graham)

Lighter molecules diffuse and equilibrate faster than heavier molecules

Density of oxygen and carbon dioxide

O2 1.43 g/L; CO2 1.96 g/L

O2 vs CO2 diffusion in a gas (alveolus)

O2 diffuses 1.17 times faster than CO2 (because it is lighter)

Graham's relative rate: O2 (MW 32) vs CO2 (MW 44)

Ratio = 1.17 : 1; O2 diffuses through gas 1.17 times faster than CO2

Diffusion of gas through a liquid depends on

Inversely proportional to the square root of density (MW) and directly proportional to the solubility coefficient

Physiologic solvent, temperature, and pressure for diffusion

Solvent is plasma; temperature is body temperature; pressure is 1 atmosphere

CO2 vs O2 diffusion across the AC membrane

CO2 is about 19-20 times more diffusible than O2

Relative solubility of CO2 vs O2 (slide 25 numbers)

0.592 / 0.0244 = about 24: CO2 is about 24 times more soluble than O2

Overall: how much faster does CO2 cross the AC membrane than O2?

About 20 times faster (combining weight, solubility, diffusion in gas and liquid)

Why does CO2 diffuse faster through liquid despite being heavier? (notes)

Its much higher solubility more than compensates for its higher molecular weight

Summary: what determines O2 dissolving in plasma?

Mainly the PAO2

Summary: what determines CO2 dissolving in plasma?

Mainly the level of alveolar ventilation (air in/out)

Fick's First Law of Diffusion

Describes bulk movement of gas through a biological membrane

Fick's Law elements

A = cross-sectional area; D = diffusion coefficient of the gas; T = thickness of the membrane; (P1 - P2) = partial pressure gradient across the membrane

According to Fick's Law: greater surface area

More diffusion

According to Fick's Law: greater diffusion constant

More diffusion

According to Fick's Law: greater pressure gradient

More diffusion

According to Fick's Law: greater distance (thickness) across the membrane

Less diffusion

What mainly determines diffusion in a normal lung?

Gas pressure gradients, because area and thickness of the AC membrane are relatively constant in healthy people

Diffusion coefficient in Fick's Law

Derived from Graham's law (inverse to molecular weight) and Henry's law (direct to solubility)

Edema at the AC membrane

Thickens the membrane and slows diffusion

Which gas is affected first by AC membrane defects?

Oxygen; defects limit O2 long before CO2 because CO2 already diffuses about 20 times better

Does the AC membrane limit CO2 diffusion clinically?

No; in a clinical sense, the AC membrane never limits diffusion of CO2 from blood to alveoli

Conditions that thicken the AC membrane and present as an O2 problem

Pulmonary fibrosis and sarcoidosis

Pulmonary fibrosis (notes)

Thickening and scarring of the AC membrane

COPD and the AC membrane (notes)

The opposite: the membrane is overly thin/stretched

Important caution about AC membrane O2 problems

Do not interpret this to mean there are no CO2 issues (CO2 problems can arise from other causes, such as ventilation)