The data below has been taken for the reaction of a dye with the hydroxide ion. The reaction was performed at two different hydroxide ion concentrations while the dye concentration was kept constant. What is the rate law?
[OH─] = 0.10 M [OH─] = 0.20 M
t (min) Abs ln(Abs) Abs ln(Abs)
0 1.000 0.000 1.000 0.000
1 0.905 -0.100 0.678 -0.389
2 0.811 -0.209 0.451 -0.796
3 0.735 -0.308 0.288 -1.245
4 0.664 -0.409 0.185 -1.687
To determine the rate law, we need to examine how the rate of the reaction changes with the concentration of the hydroxide ion ([OH-]).
First, let's calculate the initial rate of the reaction at both hydroxide ion concentrations. We can use the change in absorbance (Abs) divided by the change in time (t) to find the average rate of reaction over the specified time intervals.
For [OH-] = 0.10 M:
Initial Rate = (Abs2 - Abs1) / (t2 - t1)
= (0.905 - 1.000) / (1 - 0)
= -0.095
For [OH-] = 0.20 M:
Initial Rate = (Abs2 - Abs1) / (t2 - t1)
= (0.678 - 1.000) / (1 - 0)
= -0.322
Next, let's examine the relationship between the rate of reaction and the hydroxide ion concentration. We should focus on one hydroxide ion concentration at a time and compare the rate of reaction at different time points.
For [OH-] = 0.10 M:
When the reaction was performed at two different times, the change in absorbance (Abs) and the natural logarithm of absorbance (ln(Abs)) are as follows:
t (min) Abs ln(Abs)
0 1.000 0.000
1 0.905 -0.100
2 0.811 -0.209
3 0.735 -0.308
4 0.664 -0.409
From the table, we can observe that as the reaction progresses, the absorbance decreases and its natural logarithm decreases as well. This suggests that the reaction follows first-order kinetics with respect to [OH-], meaning the rate is directly proportional to [OH-].
For [OH-] = 0.20 M:
When the reaction was performed at two different times, the change in absorbance (Abs) and the natural logarithm of absorbance (ln(Abs)) are as follows:
t (min) Abs ln(Abs)
0 1.000 0.000
1 0.678 -0.389
2 0.451 -0.796
3 0.288 -1.245
4 0.185 -1.687
Similar to the previous case, as the reaction progresses, the absorbance decreases, and the natural logarithm of absorbance decreases as well. Hence, the reaction also follows first-order kinetics with respect to [OH-] at [OH-] = 0.20 M.
Combining the information from both concentrations, we can conclude that the rate law for this reaction is first-order with respect to [OH-]. The rate law can be represented as:
Rate = k[OH-]
where k is the rate constant.