A student is pedaling a stationary bicycle at the U of M Rec Center. Her alveolar PO2 = 115 mm Hg and her oxygen consumption is 1.0 liter/min. If the inspired PO2 = 150 mm Hg and the barometric pressure is 747 mm Hg, what is her alveolar ventilation?

This is an alveolar gas equation question and it is used to approximate the partial pressure of oxygen in the alveolus (PAO2):

The equation states;

PₐO₂ = P₁O₂ - (PₐCO₂/R) = [ (PB - PH₂O) * F₁O₂ - (PₐCO₂/R) ] ... Eqn 1

where

PₐO₂ = Alveolar partial pressure of O2 = 115mmHg

P₁O₂ = Inspired partial pressure of O2 = 150mmHg

PB = barometric pressure,

PH₂O = Water vapor pressure (usually 747 mmHg),

F₁O₂ = fractional concentration of inspired oxygen,

and R = gas exchange ratio. (Usually around 0.8)

FₐO₂ = Fraction of alveolar O₂

(O₂) = 1L/min = 1dm³

From eqn 1. we have

PₐCO₂ = (P₁O₂ - PₐO₂) / R

= (150 - 115) x0.8

PₐCO₂ = 28mmHg

Similarly from Eqn 1, we have

F₁O₂ = (PₐO₂ + PₐCO₂/R) / (PB - PH₂O)

F₁O₂ = (115 + (28/.8)) / (747 - 47)

F₁O₂ = 0.21

Now to find the Alveolar Ventilation A, we will use this equation;

O₂ = A (F₁0₂ - FₐO₂) ... Eqn 2

But FₐO₂ = PₐO₂ / (PₐO₂ + PₐCO₂)

FₐO₂ = 115 / (115+28) = 0.8

A = O₂ / (F₁0₂ - FₐO₂)

A = 0.001 / (0.21 - 0.8)

A = 0.00169m³/min

Hence, the aveolar ventilation is 0.00169m³/min