Q: “How many metric tons of CO2 is 1 ppm in our atmosphere?”
A: tl;dr: about eight billion.
DETAILS:
The Earth's atmosphere is variously estimated to have a mass of
5.1 to
5.3 × 10¹⁸ kg. (The 5.1 figure is from Trenberth & Smith 2005; the 5.3 figure is from several older sources.)
Using the “5.3” estimate, that’s 5.3 × 10⁶ Gt = 5.3 million gigatonnes.
So, one ppmm (part-per-million by mass) weighs one-millionth of that, or about 5.3 Gt.
However, atmospheric gas concentrations are customarily expressed in ppmv (parts-per-million by volume, a/k/a molar fraction, µ mol / mol), rather than ppmm. To calculate the mass of one ppmv requires scaling according to the molecular weight of the gas in question. (Note: if water vapor is ignored this is properly called the “dry molar fraction.”)
The average molecular weight of the Earth's atmosphere is 28.966 g/mole (~29). So, for carbon dioxide, 1 ppmv CO2 (molecular wt 44.01) has mass ≈(44/29) × 5.3 Gt = 8.053 Gt, of which 12/44-ths or 2.196 Gt
† is carbon.
1 Pg (petagram) = 1 Gt (gigatonne), so 1 PgC (“petagrams carbon”) is contained in (44/12) = 3.667 Gt CO2, and is equivalent to 3.667/8.053 = 0.4553 ppmv CO2 in the atmosphere. 415 ppmv CO2 (the current approximate average atmospheric concentration) has mass 415 × 8.053 Gt/ppmv = 3,342 Gt. That much CO2 contains (12/44)×3342 = 911 PgC.
Using the “5.1” estimate of Trenberth & Smith 2005 for atmospheric mass yields a slightly different result of (5.1/5.3)×8.053 = 7.75 Gt/ppmv CO2, and (5.1/5.3)×2.196 = 2.11 PgC per ppmv CO2.
IPCC AR5 WGI
uses a similar figure: 2.12 PgC per ppmv CO2 (from
Prather et al, 2012). Using that figure, the answer would be (2.12/2.196)×8.053 = 7.77 Gt/ ppmv CO2.