Alveolar carbon dioxide is inversely proportional to alveolar ventilation
Expansion
Alveolar ventilation = (tidal volume - dead space) x respiratory rate
For a typical adult: (500 - 150) x 12 = about 4.2 litres per minute, against a minute ventilation of 6 litres.
Alveolar PCO2 = (carbon dioxide production x constant) / alveolar ventilation
So arterial carbon dioxide is determined only by carbon dioxide production and alveolar ventilation. Since production is relatively stable, PaCO2 is the direct index of alveolar ventilation: a raised value always means hypoventilation relative to production.
The relationship also shows why breathing pattern matters. Compare two patients with the same 6 litre minute ventilation:
- 500 ml x 12 gives alveolar ventilation of 4.2 litres
- 250 ml x 24 gives (250 - 150) x 24 = 2.4 litres
The second patient hypoventilates despite an identical minute volume, because dead space consumes a far larger share of each breath.