12.806 / 10.571 Atmospheric Physics and Chemistry
(Distributed April 4, 2006 and due April 11, 2006)
Problem 1
Say you are downwind from a large SO
2
“source region” in which the SO
2
concentration [SO
2
] (0) is 3 x 10
11
molecule cm
–3
in the lowest h kilometers and zero
above that. There are no additional sources between you and this source region and the
wind vector is horizontal (x direction) and constant in time. Assume that SO
2
is removed
by reaction with OH in the gas phase to produce H
2
SO
4
. Derive a formula for P (= the
rate of production per unit area of H
2
SO
4
) in the downwind region as a function of h,
τ
=
SO
2
chemical lifetime = 1/
l
[OH] [M],
l
= third order rate constant, u = wind speed, and x
= distance from source region. State briefly the major assumptions used in deriving your
formula.
Graph P as a function of x from 0 km to 1000 km from the source for u = 3.3
m/sec, h = 1.9 km,
l
= 2 x 10
–31
cm
6
molecule
–2
sec
–1
, and [OH] = 2 x 10
6
radicals cm
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 Spring '03
 RogerD.Kamm
 Mole, pH, Steady State, Chemical reaction, Rate equation, source region

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