Natural sources add sulfur dioxide (SO_2) to the atmosphere at a rate of about 1
ID: 943936 • Letter: N
Question
Natural sources add sulfur dioxide (SO_2) to the atmosphere at a rate of about 10^8 metric tons of S per year. The background concentration of atmospheric SO_2, measured in remote areas where anthropogenic sources are not likely to have much influence, is about 0.2 parts per billion, by volume (ppb(v)]. What is the residence time, in days, of atmospheric SO_2 in remote regions? Useful info: molar mass of air = 28.96 g/mol, mass of Earth's atmosphere is 5.14 Times 1021 g, and ppb(v) is equivalent to mole fraction.Explanation / Answer
Residence time is the average time that a particle spends in a particular system.
T=V/q
Where T=residence time of a particle in a system
V=capacity of the system
q=flow rate of the substance from the system
for the given system that is the earth’s atmosphere the particle added is SO2,
q=10^8 metric tons /year of S =10^8 metric tons/year* 1000Kg/metric ton=10^11 kg /year=10^11*10^3 g/year=10^14 g/year =(10^14 g/year )/(32 g/mol) of S=0.0312*10^14 mol/year of S=0.0312*10^14 mol/year of SO2 (since 1 mole of SO2 contains 1 mol of S)
V=mole fraction of SO2 in remote areas (as it is the capacity of the atmosphere to hold SO2)* moles of air=0.2*5.14*10^21g/28.96g/mol=0.0355*10^21 mol of SO2 can be held by the atmosphere
T=(0.0355*10^21 mol)/(0.0312*10^14 mol/year)=1.138*10^7 year=1.138*10^7 year *365 days/year=415.37 *10^7 days =4.15*10^9 days (answer)
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