Just do the math: (lung volume) x (density of air) = mass of air in lungs.
Of course, we have to consider — since most of us cannot directly measure our lungs’ capacity — a number of factors such as age, sex, height, weight for lung capacity and such as temperature and humidity for density of air, but we can simplify the thinking and calculations by averaging and generalizing.
“In Normal Standards for Lung Volumes, Intrapul-monary Gas-mixing, and Maximum Breathing Capacity” (Thorax (1954), 9, 313), Needham, Rogan, and McDonald reported the following statistics about “vital capacity” in Table V (given as mean +/- standard deviation):
3.45 L +/- 0.98 L for men aged 11-19 or 0.91 +/- 0.26 gallon
2.88 L +/- 0.63 L for women aged 11-19 or 0.76 +/- 0.17 gallon
4.13 L +/- 0.75 L for men aged 20 and above or 1.09 +/- 0.20 gallon
2.76 L +/- 0.54 L for women aged 20 and above or 0.73 +/- 0.14 gallon
And the following about “total lung capacity” in Table V (given as mean +/- standard deviation):
4.59 L +/- 1.3 L for men aged 11-19 or 1.21 +/- 0.34 gallon
3.88 L +/- 0.8 L for women aged 11-19 or 1.02 +/- 0.21 gallon
6.23 L +/- 0.83 L for men aged 20 and above or 1.65 +/- 0.22 gallon
4.33 L +/- 0.62 L for women aged 20 and above or 1.14 +/- 0.16 gallon
The density of air is about 1.2 g/L (at 20ºC (68ºF) and 1 atm of pressure (14.7 psi, 29.92 in Hg). A table of air density values at different temperatures can be found on Wikipedia. Note also that 1 gram = 0.00220462 pounds 0.035274 ounces.
Now that we have the numbers, we can plug them in the formula: (lung volume) x (density of air) = mass of air in lungs.
Calculating for “vital capacity,” we find:
4.14 +/- 1.8 g for men aged 11-19 or 0.15 oz +/- 0.04 oz
3.46 +/- 0.76 g for women aged 11-19 or o.12 +/- o.027 oz
4.96 +/- 0.9 g for men aged 20 and above or o.17 +/- 0.032 oz
3.31 +/- 0.65 g for women aged 20 and above or 0.11 +/- 0.023 oz