Untitled - Kelly Walsh High School

192 CHEMISTRY FOR THE UTTERLY CONFUSED
Canceling the rate constants and the [0.01] m and simplifying gives:
Therefore, the rate equation is: Rate k[NO] 2 [O 2]
The rate constant, k, could be determined by choosing any of the three experiments,
substituting the concentrations, rate, and orders into the rate expression,
and then solving for k.
13-3 Integrated Rate Laws (Time and
Concentration)
So far, we have used only instantaneous data in the rate expression. These
expressions allow us to answer questions concerning the speed of the reaction
at a particular moment, but not questions like about how long it might take to
use up a certain reactant. However, if we take into account changes in the concentration
of reactants or products over time, as expressed in the integrated
rate laws, we can answer these types of questions.
Consider the following reaction: A l B
Assuming this reaction is first order, we can express the rate of reaction as the
change in concentration of reactant A with time:
Rate [A]
t
1
Q1
2 2 Rn Thus, n 1
in addition to the rate law: Rate k[A]
Setting these terms equal gives: and integrating over time gives:
[A]
k[A]
t
ln [A] 0
kt
[A] t
where, ln is the natural logarithm, [A] 0 is the concentration of reactant A at
time 0 and [A] t is the concentration of reactant A at some time t.
If the reaction is second order in A, we can derive the following equation using
the same procedure:
1
[A] t
1
kt
[A] 0
Hydrogen iodide, HI, decomposes through a second-order process to the elements.
The rate constant is 2.40 10 21 /M s at 25°C. How long will it take for