Question

Nitrous oxide is produced by bacteria in the natural denitrification process. It is chemically inert in the troposphere, but in the stratosphere it is degraded photochemically. The average concentration of N₂O in the troposphere is about 250 ppb, and its residence time there is 10 years. What is the global rate of production of N₂O in units of kg/year? Assume a temperature of 0.00 °C and a pressure of 1.00 atm. Assume that the volume of the troposphere (at 0.00 °C and 1.00 atm) is 90% of that of the atmosphere (4.30*10²¹ L).

Answer 1

Given the volume of the troposphere is 90 percent of the volume of the atmosphere.

Volume of the troposphere = (0.9)*(4.30 X 10²¹) = 3.87 X 10²¹ L

Note : 1 g = 10⁶g and Moles = Weight/Molecular weight

250 ppb = 250 g/L = (250 X 10^-6) g/L = (250 X 10^-6)/44 = 5.68 X 10^-6 mol/L

Note that the molecular mass of N₂O is 44 g/mol used in the calculation above.

Now using the formula for molarity, M = Moles/Volume(in L)

5.68 X 10^-6 = Mass/(44 X Volume of troposphere)

5.68 X 10^-6 = Mass/(44 X 3.87 X 10²¹)

Mass of N₂O = 9.67 X 10¹⁷ gm = 9.67 X 10¹⁴ kg

Rate = Mass(in kg)/Time(in years)

Rate = (9.67 X 10¹⁴)/10 = 9.67 X 10¹³ kg/year