Gas Laws and Diffusion

State Dalton’s Law

The total pressure of a gas mixture equals the sum of the partial pressures of each gas.
Pgas = Fgas × PB

Why must PH₂O be subtracted when calculating inspired gas partial pressure?

Because inspired air becomes fully humidified; water vapor takes up 47 mmHg of pressure and displaces other gases

Calculate PIO₂ at sea level (PB = 760) on room air using humidified formula

PIO₂ = 0.21 × (760 – 47) = 149.7 mmHg

What happens to partial pressures at high altitude?

Barometric pressure decreases → all partial pressures decrease → ↓ PAO₂ → ↓ PaO₂

State Fick’s Law of Diffusion

Vgas = A × D × (P1 − P2) / T
Gas diffusion increases with ↑ area and ↑ gradient, and decreases with ↑ membrane thickness

How does COPD affect Fick’s Law?

↓ Surface area (destroyed alveoli) → ↓ Vgas → ↓ O₂ diffusion → hypoxemia, hypercapnia

How does pulmonary fibrosis affect Fick’s Law?

↑ membrane thickness → ↓ Vgas → diffusion limitation for O₂

Why does CO₂ diffuse faster than O₂?

CO₂ has higher solubility → its diffusivity is ~20× greater

State Henry’s Law

Gas dissolved in a liquid is proportional to its partial pressure.
Higher Pgas → more dissolves

Why does CO₂ dissolve in blood more easily than O₂?

CO₂ is FAR more soluble in liquid

State Graham’s Law

Diffusion rate ∝ 1 / √(molecular weight).
Lower MW = faster diffusion

Why does O₂ diffuse faster than CO₂ by molecular weight?

O₂ has lower MW → faster.
BUT CO₂ still diffuses faster overall due to solubility

Direction of normal gas movement?

O₂: Alveoli (PAO₂) → blood (PaO₂)
CO₂: Blood (PaCO₂) → alveoli (PACO₂)

What creates the driving force for O₂ diffusion?

The difference between PAO₂ (~100) and PaO₂ (~80–100)

What increases the rate of diffusion the MOST?

Increasing ΔP (pressure gradient)

State the Alveolar Gas Equation

PAO₂ = FiO₂ (PB – 47) – (PaCO₂ / R)

What does the alveolar gas equation calculate?

Expected alveolar oxygen (PAO₂)

If FiO₂ = 0.21, PB = 760, PaCO₂ = 40, R = 0.8 → calculate PAO₂

PAO₂ = 0.21 (760–47) – (40/0.8)
= 149.7 – 50
= 99.7 mmHg

Why is R assumed to be 0.8?

Normal mixed diet = normal respiratory exchange ratio

State the A–a gradient formula

A–a = PAO₂ – PaO₂

What is a normal A–a gradient?

5–15 mmHg (increases with age)

What does a high A–a gradient indicate?

V/Q mismatch or diffusion impairment

Is elevated A–a gradient seen in hypoventilation?

No — hypoventilation causes low PaO₂ with normal A–a gradient

Causes of physiological shunt?

• Atelectasis

• Pneumonia

• Pulmonary edema

• Obstruction

• Bronchospasm

• Pneumothorax

Why does oxygen NOT correct shunt hypoxemia well?

Blood bypasses ventilated alveoli → no access to oxygen

HIGH V/Q (DEAD SPACE-LIKE)

Ventilation without perfusion

Causes of high V/Q (relative dead space)?

• Positive pressure ventilation

• Low cardiac output

• Emphysema (destroyed capillaries)

LOW V/Q (SHUNT-LIKE)

Perfusion without ventilation

Classic example of absolute dead space?

Pulmonary embolism

State the Modified Bohr Equation

VD/VT = (PaCO₂ – PECO₂) / PaCO₂

What does VD/VT measure?

Physiologic dead space fraction

Normal VD/VT value?

0.30

If PaCO₂ = 40 and PECO₂ = 28, calculate VD/VT

VD/VT = (40 – 28) / 40 = 0.30

What is perfusion-limited gas exchange?

Gas diffusion stops once blood equilibrates with alveoli. Limited by blood flow, not membrane

What is diffusion-limited gas exchange?

Gas does not reach equilibrium due to thickened membrane or ↓ surface area

Which limitation is normal O₂ and CO₂ under?

O₂: perfusion-limited (normal)
CO₂: perfusion-limited (normal)

When does O₂ become diffusion-limited?

• Pulmonary fibrosis

• Emphysema

• Exercise (↓ transit time)

• Thickened AC membrane

Why does exercise reduce O₂ diffusion reserve?

Transit time drops from 0.75s → 0.25s

In healthy people, does exercise cause hypoxemia?

No — they still equilibrate before leaving alveoli

Why does exercise cause hypoxemia in fibrosis patients?

Thick membrane + reduced transit time → no time for equilibration → ↓ PaO₂

Why does CO₂ diffuse faster than O₂?

CO₂’s solubility is much higher

Which variable in Fick’s Law is most affected by emphysema?

Surface area (A ↓↓)

Which variable in Fick’s Law is most affected by pulmonary fibrosis?

Thickness (T ↑↑)

Which V/Q problem causes refractory hypoxemia?

Shunt (low V/Q)

In high V/Q, what happens to PaCO₂?

Usually normal (CO₂ compensates better)

In high V/Q, PaO₂ is?

Low — O₂ is more sensitive to changes in perfusion

Calculate PO₂ in dry atmospheric air at sea level (PB = 760)

PO₂ = 0.21 × 760 = 159.6 mmHg

Calculate PH₂O at body temperature

47 mmHg (constant)

Calculate PIO₂ (inspired O₂) at sea level

PIO₂ = 0.21 × (760 – 47)
PIO₂ = 0.21 × 713 = 149.7 mmHg

Calculate PIO₂ at 500 mmHg barometric pressure

PIO₂ = 0.21 × (500 – 47)
= 0.21 × 453
= 95 mmHg

Calculate partial pressure of nitrogen in humidified air (FiN₂ = 0.79)

PN₂ = 0.79 × (760 – 47)
= 0.79 × 713 = 563 mmHg

ALVEOLAR GAS EQUATION Formula:

PAO₂ = FiO₂ (PB – 47) – (PaCO₂ / R)
R = 0.8 unless stated

FiO₂ 21%, PB 760, PaCO₂ 40 → PAO₂?

PAO₂ = 0.21(760–47) – 40/0.8
= 150 – 50
= 100 mmHg

FiO₂ 40%, PB 760, PaCO₂ 50 → PAO₂?

PAO₂ = 0.40(760–47) – 50/0.8
= 0.40(713) – 62.5
= 285 – 62.5
= 222.5 mmHg

A–a GRADIENT CALCULATIONS Formula:

A–a = PAO₂ – PaO₂

If PAO₂ = 100 and PaO₂ = 85 → A–a?

15 mmHg (upper limit of normal)

PAO₂ = 150, PaO₂ = 70 → A–a?

80 mmHg (abnormal)

PAO₂ = 220, PaO₂ = 110 → A–a?

110 mmHg (severe V/Q mismatch)

MODIFIED BOHR EQUATION (DEAD SPACE)  Formula:

VD / VT = (PaCO₂ – PECO₂) / PaCO₂

PaCO₂ 40, PECO₂ 28 → VD/VT?

(40–28)/40 = 0.30

PaCO₂ 50, PECO₂ 20 → VD/VT?

(50–20)/50 = 0.60 (high dead space)

PaCO₂ 60, PECO₂ 10 → VD/VT?

(60–10)/60 = 0.83 (fatal range)

If surface area is cut in half, diffusion rate becomes:

↓ by 50%

PECO₂ must always be __________ than PaCO₂

Lower (because of dead space dilution)