Page 157 - Basic physical chemistry for the atmospheric sciences

Photochemistry 143

If Reactions (7. 1 7 b) and (7. 1 7 c) occur one million times for each Cl(g)
molecule produced in Reaction (7. 1 7 a), what is the overall quantum
yield of HCl?
.
Solution. Reactions (7 1 7) are an example of a chemical chain reac­
tion. The chain is initiated by Reaction (7. 1 7 a) ; then Reactions (7. 1 7 b)
and (7. 1 7 c) continue to produce HCl(g) until either the H(g) or Cl(g) is
removed (by, for example , H + H � H 2 or Cl + C l � Cl ) . How­
2
ever , if the Reactions (7. I 7b) and (7. 1 7c) occur 1 0 6 times for each Cl(g)
6
molecule produced by Reaction (7. 1 7a), 10 moles of HCI(g) will be
produced for every einstein of radiation absorbed in Reaction (7. 1 7a).
Therefore, <l>ttci = 1 0 6 •

7 .4 Rate coefficients for photolysis
Following the ideas discussed in Section 3 . 1 , we could express the
reaction rate for a photochemical reaction, such as Reaction (7.6), in
the form
.
Reaction rate = k[NOi(g)]"'[h v]n (7 1 8)
where k is the rate coefficient and m + n is the overall order of
)
the reaction. Experiments show that for Reaction (7 .6 , m = n = I .
However , as we have seen , the reaction rate for a photochemical
reaction generally varies sharply with the energy of the photon v , and
h
it will also depend on the flux of the photons and the quantum effi­
ciency. This complication can be avoided if we consider a constant
flux of photons with a fixed distribution with respect to wavelength
and combine this with k to give
Reaction rate = j [NOi(g)] (7. 1 9)

wherej is a pseudo first-order rate coefficient called the photolytic rate
coefficien . (Note: Photolytic rate coefficients are generally repre­
t
s
sented by the symbolj, and are sometimes called j-value . )
Exercise 7.4. When the s u n is overhead i n midlatitudes , a typical
3
value of j in Eq. (7 1 9) is 5 .0 x 1 0 - s - 1 • If Reaction (7 .6) is the only
.

sink for N0 2 (g), what i s its residence time in the atmosphere under
these conditions? Under these same conditions, how many molecules
of NO(g) per cubic meter of air at 1 . 0 atm and 20°C will be produced
in 1 hour by Reaction (7 .6) if the concentration of NOi(g) is 0.50 parts
per billion by volume (ppbv) of air?