Global warming potential

The Global warming potential numbers are expressed by mass: The GWP of CH4 is 84, meaning that 1kg of CH4 has the same global warming potential as 84 kg CO2.

But the concentrations you'll see of CO2, CH4, etc are usually expressed in parts per million (PPM) or parts per billion (PPB), ie molar fractions.

Here I've calculated the Global Warming Potential numbers for gasses of the same molar fraction (PPM or PPB).

To start, let's calculate the GWP by molar fraction of CH4 the hard way, by calculating the mass of 1 PPM CH4 in 1 m3 of gas, multiplying that by 84 to calculate the mass of the equivalent CO2, converting that back to PPM fraction of CO2.

A m3 of gas at 25 °C contains 1/0.024789598=40.34 mol gas, and if that gas contains 1ppm CH4, that will be 40.34e-6 mol CH4. One molecule of CH4 weighs 12+4=16 atomic mass units, so 40.34 mol of CH4 weighs 40.34e-6* 6.022e23 * 16 * 1.66053906660e-27 = 6.45 mg.

Given the GWP of CH4 is 84, these 6.45 mg of CH4 has the same effect as 84*6.45 mg = 54.2 mg CO2. One molecule of CO2 weighs 12+2*16 = 44 atomic mass units, so 54.2 mg is 54.2e-6 / (44*1.66053906660e-27)=7.42e20 atoms, or 1231.8 umol. As there are 40.34 mol in the m3, this is 1231.8/40.34 = 30.5 ppm of CO2.

So 1 ppm CH4 has the same effect as 30.5 ppm CO2.

We could have reached that conclusion faster: 1 ppm CH4 weighs 16/44 as much as 1 ppm CO2, so if the GWP of CH4 is 84 for the same weight, it should be 16/44 *84 for the same fraction. And 16/44*84=30.5.

Gas	molecular mass [au]	GWP 20 year (same mass)	GWP 20 year (same ppm)	GWP 100 year (same mass)	GWP 100 year (same ppm)	Source
Methane CH4	12+4=16	96	34.9	32	11.6	2013 GRL
Nitrous oxide (N2O)	14+2*16=46	289	302	292	305	2007 p212
SF6	32+19*6=146	16300	54086	22800	75654	2007 p212