This approach to finding reaction order is
called the method of initial rates, since it relies on fixing theconcentration at specific initial values and measuring the initial
rate associated with each concentration.
So far we have considered only reactions which
have a single reactant. Consider a second example of the method ofinitial rates involving the reaction of hydrogen gas and iodine
gas:
In this case, we expect to find that the rate
of the reaction depends on the concentrations for both reactants.As such, we need more initial rate observations to determine the
rate law. In
,
observations are reported for the initial rate for three sets ofinitial concentrations of
and
.
Hydrogen gas and iodine gas initial rate data at 700k
| Experiment |
(M) |
(M) |
Rate (M/sec) |
| 1 |
0.10 |
0.10 |
|
| 2 |
0.20 |
0.10 |
|
| 3 |
0.20 |
0.20 |
|
Following the same process we used in the
example, we write the general rate law for the reaction as
By comparing experiment 1 to experiment 2, we
can write
This simplifies to
from which it is clear that
.
Similarly, we can find that
.
The reaction is therefore first order in each reactant and issecond order overall.
Once we know the rate law, we can use any of
the data from
to
determine the rate constant, simply by plugging in concentrationsand rate into
. We find that
.
This procedure can be applied to any number of
reactions. The challenge is preparing the initial conditions andmeasuring the initial change in concentration precisely versus
time.
provides an
overview of the rate laws for several reactions. A variety ofreaction orders are observed, and they cannot be easily correlated
with the stoichiometry of the reaction.
Rate laws for various reactions
| Reaction |
Rate Law |
|
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Concentrations as a function of time and the reaction
half-life
Once we know the rate law for a reaction, we
should be able to predict how fast a reaction will proceed. Fromthis, we should also be able to predict how much reactant remains
or how much product has been produced at any given time in thereaction. We will focus on the reactions with a single reactant to
illustrate these ideas.
Consider a first order reaction like
,
for which the rate law must be
From Calculus, it is possible to use
to find the function
which tells us the concentration
as a function of time. The result is
or equivalently
reveals that, if a reaction is first order, we can plot
versus time and get a straight line with slope equal to
.
Moreover, if we know the rate constant and the initialconcentration, we can predict the concentration at any time during
the reaction.
