The 1987 Montreal protocol was the first international agreement to control emissions of harmful chlorofluorocarbons (CFCs) to the ozone layer. It was subsequently amended (London 1990, Copenhagen 1992) to respond to the increased urgency created by the antarctic ozone hole. In this problem we compare the effectiveness of the original and amended protocols. We focus on CFC-12, which has an atmospheric lifetime of 100 years against loss by photolysis in the stratosphere. We start our analysis in 1989 when the Montreal protocol entered into force. In 1989 the mass of CFC-12 in the atmosphere was m = 1 × 1010 kg and the emission rate was E = 4 × 108 kg yr-1. (a) The initial Montreal protocol called for a 50% reduction of CFC emissions by 1999 and a stabilization of emissions henceforth. Consider a future scenario where CFC-12 emissions are held constant at 50% of 1989 values. Show that the mass of CFC-12 in the atmosphere would eventually approach a steady-state value m = 2 × 1010 kg, higher than the 1989 value. Explain briefly why the CFC-12 abundance would increase even though its emission decreases.
(b) The subsequent amendments to the Montreal protocol banned CFC production
completely as of 1996. Consider a scenario where CFC-12 emissions are held constant from 1989 to 1996 and then drop to zero as of 1996. Calculate the masses of CFC-12 in the atmosphere in years 2050 and 2100. Compare to the 1989 value.