How much gas is exchanged in one human breath?
According to Wikipedia  


  "In a healthy, young adult, tidal volume is approximately 500 ml per inspiration..." 


(tidal volume is the volume inspired/expired)

Using this figure, together with values for gas composition also taken from Wikipedia, I estimate that in each breath we take in 18 mg O2 (1.1 mmol) and we release 36 mg of CO2 (1.2 mmol) plus 20 mg H2O (1.1 mmol). These are, as you say, ballpark figures.

Sample calculation:

O2 inspired = 21% by volume; O2 expired = 16% by volume

O2 change = 5% by volume = 5*500/100 = 25 mL

1 mole gas = 22.4 L; 1 mmol gas = 22.4 mL

O2 change = 25/22.4 mmol = 1.1 mmol

MW O2 = 16

O2 change = 17.6 mg

The relative values are reassuringly close to what you might predict from the textbook equation for oxidation of carbohydrate: C6H12O6 + 6O2 -> 6CO2 + 6H2O