Question

Natural sources add sulfer dioxide (SO2) to the atmosphere at a rate of about 1E8 tonnes (S)/yr. The background concentration of atmospheric SO2. Measured in remote areas where anthropgenic sources are note likely to have much influence, is about .4 parts per billion, by volume. What is the residence time of atmospheric SO2 in the remote regions (in days)?

Calculate mass of atmosphere, # mol air, # mol S)2, residence time

Answer 1

First, 1 E8 tonnes = 100 E12 grams.

Mass of atmosphere = 5.14 E21 g ..directly use it or derive as follows

Approximating Earth's atmosphere as a layer of gas 7.5 km thick, with uniform density 1.3 kg/m^3

Rearth + 7.5 km = Rtotal

Vatm = Vtotal - Vearth

Since we now know the volume and density of the atmosphere, multiply the two to find the mass.

Vatm * 1.3 KG/m^3 = Total mass of the atmosphere

Mass of atmosphere = 5.14 E21 g

moles in atmosphere = 5.14 E 21 g * (1 mol air / 29 g) = 177.2 E 18
moles air in atmosphere

NO2 is .4 ppbv

177.2 E18 moles air * (.4 part SO2/ 1 E9 parts air) = 70.88 E9 moles
SO2 in atmosphere

70.88 E9 moles SO2 *(64 g SO2/1 mol SO2) = 4.536 E12 g SO2 in atmosphere=2.2268 E12 g S in atmosphere

2.2268 E12 g S / (100 E12 grams S/year) = 0.02268 years

in days, 0.02268 years * (365 days / 1 year) = 8.2782 days