Page 58 - Basic physical chemistry for the atmospheric sciences

44 Basic physical chemistry
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It is clear from Exercise . 1 that for the general chemical reaction
.
aA + bB + . . �gG + hH . . . (3. 1 )
we have
I d[A] I d[B] I d[G] I d[H]
· · · (3 . 2 )
a dt b dt g dt h dt
where [A] , [B] , . . . are the molar concentrations. Hence, any one of
the quantities in Eq. (3.2) is referred to as the reaction rate for Reac­
tion (3 . 1 ) . The reaction rate is usually expressed in units of mol L - 1
1 1 , where M is molarit ) .
y
s - (or M s -
M a n y reactions occur at a decreasing rate with increasing time. This
is because the reaction rate diminishes as the concentrations of the
reactants diminish. For Reaction (3 . 1 ) , the reaction rate can often be
expressed as
Reaction rate = k[Ar[B]" . . . (3 . 3 )

Equation (3 . 3 ) is called the rate law or rate equation for Reaction
(3 . 1 ) . The exponents m and n are generally integers or half-integers ; m
is called the order of the reaction with respect to A , and n the order
with respect to B , etc. The overall order of the reaction is m + n + . . . .
, n , . . . must be determined experimentally, because,
The orders m
in general , they cannot be predicted theoretically or deduced from
Reaction (3. 1 ) .
The term k i n Eq . (3 . 3 ) i s called the rate coefficient (or, more
formally, the specific reaction rqte coefficient, since it is numerically
equal to the rate of reaction if all concentrations were unity). Each
reaction is characterized by a value of k at each temperature. The
units of k depend on the overall order of the reaction .
, n, . . . in Eq. (3 . 3 )
One method for determining the exponents m
is from the initial reaction rates for several different sets o f initial
concentrations of A, B , . . . . For example, if when [A] is doubled, and
s
[B] . . . are held constant, the initial reaction rate double , m = I ; if it
3
quadruples, m = 2, etc. (See Exercise . 8 . )
i
Consider a reaction that s first order in just one reactant A and for
which a = I in Reaction (3 . 1 ) . Then,
d[A]
- = k [A] (3 .4)
dt