Page 75 - Basic physical chemistry for the atmospheric sciences

Chemical kinetics

dirty water will be left in the tank, etc. Therefore, after 6 t 12 minutes
1
( 1 / 2) 6 = ( l / 64) of the dirty water will be left in the tank. If we (arbi­
trarily) decide that l/64 is a sufficiently small fraction that most of the
dirty water can be considered to have been displaced, for a chemical
that is perfectly mixed in a reservoir for which the efflux is given by a
first-order reaction [Eq. (3. 1 3)) we have the following relationships
between the renewal time ( T) , the half-life (t 12) and the residence
1
time ( T)
( 3 . 1 6 )
1
T=6t 2 =4T
1
In practice, of course, natural systems will fall somewhere between
the cases considered above of no mixing and perfect mixing.
In the ocean, elements that form insoluble hydroxides have rela­
tively short residence times (e.g. , Al and Fe have residence times in
the ocean of 1 00 and 200 years, respectively). Cation , such as
s
Na+ (aq) and K + (aq), and anions, such as c1 - (aq) and B r - (aq), have
longer residence times in the ocean (-7 x 1 0 6 to 1 0 8 years). In the
atmosphere, the very stable gas nitrogen has a residence time of a
5
million years or so, while oxygen has a residence time of , 00 0- 1 0 , 000
years. Sulfur dioxide, water, and carbon dioxide, on the other hand,
y
have residence times in the atmosphere of only a few days, 1 0 da s ,
and 4 years, respectively. O f course, residence times may e deter­
b
mined by physical removal processes (e.g. , scavenging by precipita­
tion) as well as chemical.

Exercises
i
o
3 . 7 . Answer, interpret, or explain the following n light f the
principles discussed in this chapter.
(a) A piece of paper can remain in contact with air indefi­
nitely without any observable reaction, but it reacts as
soon as it is touched with a flame.
(b) A match is stable until its head is rubbed on a rough
surface.
(c) Increasing pressure generally decreases the rates of re­
actions of solids or liquids.
(d) Increasing pressure always increases the rates of reac­
tions of gases.
(e) A catalyst is often in the form of a fine powder.