Question

CFC-11 with zero emissions Now assume that emissions had been successfully reduced to exactly zero after these peak levels in 1990 a. Given its initial levels and lifetime above, calculate what mixing ratio would be expected 25 years later in 2015, assuming perfect exponential decay. How does this calculated value compare to actual CFC-11 measurements shown for 2015 below? b. What could explain the difference between your simplified calculation and actual measurements? Northern Hemisphere Atmospheric Concentrations CFCs, CCl4 SF6 600 12 CFC-12 500 10 400 300 CFC-11 200 CCI 100 0 2020 1940 1960 1980

Answer 1

a) Since we are assuming a perfect exponential decay, the concentration reduces by a factor e^-kt with time, where t is time elapsed.

Initial concentration of CFC-11 from the graph is 275.

If emissions are zero, net input is zero, thus, concentration after decay is

k = k_oe^-kt

where k₀ is initial concentration and t is time.

To find k, we have to first find the half life of CFCs in the atmosphere, which is approximately 60 years.

Thus, when t=60, k = k₀/2.

k₀/2 = k₀e^-60k

-60k = ln(0.5)

k = 0.01155

Thus,after 25 years of exponential decay,

k = 175xe^-0.01155x25 = 131.09.

The concentration observed in the graph is 150, while calculated concentration from decay is 131.09

b) A simple explanation for the observed discrepancy would be that the net input into the atmosphere is not zero and that there are still sources of emissions of CFC11 into the atmosphere.