We will use this equation in a slightly different way, since it is difficult to define the volume V of the atmosphere. Instead, we define m = mass of Freon-11 in the global atmosphere V x C. With Vin = O and Vout = 0, we can thus write our mass balance equation as: = dm - = P - km dt where P = 1.2 x 1011 grams/year and k = 0.02 year¹.
Assume the production of Freon-11 stopped after 50 years, in the year 2010, as required by the Montreal Protocol. Solve the same mass balance equation for Period 2, namely 2010-2060, where t = 0 corresponds to 2010, and m(t = 0) for Period 2 is equal to m(t = 50) for Period 1. Note that you cannot use one expression to represent both Period 1 and Period 2; you will need to use separate equations with separate initial conditions. Also note that you cannot have a discontinuity in the curve; m(t) cannot change instantaneously in the switch from Period 1 to Period 2. Thus the initial conditions for Period 2 must equal to the ending value of m(t) at t = 50 years from Period 1.
d. Convert your expressions for m(t) for Period 1 and Period 2 into concentrations in ppb. Show the proper units on every value as you do the conversions. Use the total moles of air in the atmosphere and the molecular weight of Freon-11 to accomplish this. Write the expressions for C(t) for Period 1 and Period 2, and graph them on the same graph, as one continuous curve for 1960 – 2060.
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