1.3 Calculating Reaction Rates
Let's try an example of calculating a reaction rate. Consider the following reaction:
A → B
The following data were obtained for how the concentration of these substances changed during the experiment (see the note about units for concentration).
Time (min) |
[A] (mol ·L-1) |
[B] (mol ·L-1) |
0.0 |
1.000 |
0.000 |
3.0 |
0.400 |
0.600 |
6.0 |
0.250 |
0.750 |
We could measure the rate of the reaction either by measuring how the concentration of reactant A changes or how the concentration of product B changes. Let's measure A's average rate of change first:
rate |
= |
|
= |
(0.250 - 1.00)
(6.00 - 0.00) |
= |
– 0.125 mol · L-1· min -1 |
Compare this rate to the rate of just the first three minutes of the reaction:
rate |
= |
|
= |
(0.400 - 1.00)
(3.000 - 0.000) |
= |
- 0.200 mol · L-1· min -1 |
We can see that, as was mentioned in the last section, the rate did slow down as the overall rate is slower than the rate of the first three minutes of the reaction.
If we calculate the average rate based on the production of product B:
rate |
= |
|
= |
(0.750 - 0.00)
(6.00 - 0.00) |
= |
0.125 mol · L-1· min -1 |
Notice that we must compare rates measured during the same time period.
You will see that we got the same rate, except for the sign, when we calculated the overall average rate for the disappearance of A as for the formation of B. This is only true, however, because our balanced equation shows us that one mole of A produces one mole of B.
We would not find the same rates if we did not have a 1:1 relationship between reaction participants. For example if we examine the following reaction:
2 H2O2 → 2 H2O + O2
we find that only one mole of oxygen forms for every two moles of hydrogen peroxide that decomposes.
Therefore, we could make the following relationships:
2 H2O2 |
→ |
2 H2O |
+ |
O2 |
If 2 moles of H2O2 decompose |
then |
1 mole of O2 is formed |
||
if the rate of decomposition of H2O2 |
then |
|
the rate of formation |
|
 |
 |
Complete and check your answers to the practice questions before beginning the assignment. |
Some Comments about Units for Concentration
Concentration, as we will see in depth in our unit on Solutions, may be measured in several ways, but we will often use the unit mol ·L-1 for concentration. Be comfortable seeing this unit written in any of the following ways:
mol ·L-1 |
= |
mol / L |
= |
M |
= |
|