Using the Isolation method, we are to determine the rate law of the equation, RCOOR' + OH− → RCOO− + R'OH (where R and R' represent organic groups).
Initial concentration of experiment 1:[OH−]0 = 0.900 M
[RCOOR']0 = 0.0010 M
Initial concentration of experiment 2:[OH−]0 = 0.0015 M
[RCOOR']0 = 0.600 M
The overall rate law is: −d[RCOOR′]/dt=k[RCOOR′]^n[OH−]^m
and I found that n and m are both 1 and the pseudo constants are 35.8(for RCOOR') and 23.9(for (OH-).
I need help on finding the overall rate constant (k).
Thanks in advance
To determine the overall rate constant (k) for the reaction, you can use the experimental data and the rate law equation you have derived.
The rate law equation you have is:
−d[RCOOR′]/dt = k[RCOOR′]^n[OH−]^m
Since you have experimental data from two different experiments, you can substitute the initial concentrations and initial rates of each experiment into the rate law equation to create two equations:
Experiment 1:
Rate1 = k[RCOOR′]1^n[OH−]1^m
Experiment 2:
Rate2 = k[RCOOR′]2^n[OH−]2^m
Substituting the known values from the experiments:
Rate1 = 35.8 * [RCOOR’]1^1 * [OH−]1^1
Rate2 = 35.8 * [RCOOR’]2^1 * [OH−]2^1
You have the initial concentrations for each experiment, so you can calculate the initial rates by dividing the change in concentration over time. Let's assume the initial rate for experiment 1 is Rate1_0 and for experiment 2 is Rate2_0.
Rate1_0 = (Rate1) / (time taken for Rate1)
Rate2_0 = (Rate2) / (time taken for Rate2)
Now you have two equations with two unknowns (k and Rate1_0/Rate2_0). You can solve for k by dividing the equation for Rate1 by the equation for Rate2:
Rate1_0 / Rate2_0 = (Rate1 / Rate2)
(Rate1_0 / Rate2_0) = [RCOOR’]1 / [RCOOR’]2 * [OH−]1 / [OH−]2
Plugging in the known values for Rate1_0, Rate2_0, [RCOOR’]1, [RCOOR’]2, [OH−]1, and [OH−]2, you can solve for k:
k = (Rate1_0 / Rate2_0) / ([RCOOR’]1 / [RCOOR’]2 * [OH−]1 / [OH−]2)
By substituting the values, you can calculate the overall rate constant (k) for the given reaction.
Please note that the time taken for each rate needs to be consistent in order to get an accurate value for k.