 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-id/3/d/i/solution

For independent first-order sinks acting on the same well-mixed burden, loss frequencies add:

k_{tot} = \frac{1}{4} + \frac{1}{4} + \frac{1}{8} = \frac{5}{8} da y^{- 1}, τ_{S O_{2}} = 1.60 days .

The fraction converted to sulfate before removal by the competing direct-deposition sink is

f_{oxidation} = \frac{1/4 + 1/8}{5/8} = 0.60.

The individual event fractions are

0.40

for direct sulfur dioxide deposition,

0.40

0.20

for hydroxyl radical oxidation. These are branching fractions for the sulfur dioxide fate; sulfate formed by oxidation can subsequently be deposited as well. The argument assumes the supplied channel lifetimes are compatible effective first-order rates, not residence times of isolated air masses that never exchange.

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