The catalysed decomposition of H2O2 in aqueous solution is followed by titrating equal volume of sample solutions with KMnO4 solution at different time interval give the following results. Show that the reaction is a first order reaction.
t (mins) 0 5 15 25 45
VKMnO4 37 29.8 19.6 12.3 5.0
To determine if the catalysed decomposition of H2O2 in aqueous solution is a first-order reaction, we need to analyze the given data.
In this experiment, equal volumes of sample solutions are titrated with KMnO4 solution at different time intervals. The volume of KMnO4 solution (VKMnO4) required to fully react with H2O2 is measured at each time interval.
First, let's calculate the initial concentration of H2O2 in the sample solution at t=0 minutes.
Using the data at t=0 minutes:
VKMnO4 = 37 mL
The titration of H2O2 with KMnO4 follows the balanced chemical equation:
2KMnO4 + 3H2O2 -> 2MnO2 + 2KOH + 2H2O + 3O2
From the balanced equation, we can see that 2 moles of KMnO4 react with 3 moles of H2O2.
Assuming the concentration of KMnO4 is known, we can calculate the number of moles of KMnO4 used at t=0 minutes:
0.037 L x [KMnO4] moles/L = moles of KMnO4 used
Since 2 moles of KMnO4 react with 3 moles of H2O2, we can calculate the number of moles of H2O2 in the sample solution at t=0 minutes:
Moles of KMnO4 used x (3 moles H2O2 / 2 moles KMnO4) = moles of H2O2
Now, we can repeat this calculation for each time interval to determine the concentration of H2O2 at different time points.
Using the data at t=5 minutes:
VKMnO4 = 29.8 mL
Moles of KMnO4 used = 0.0298 L x [KMnO4] moles/L
Moles of H2O2 = Moles of KMnO4 used x (3 moles H2O2 / 2 moles KMnO4)
Repeat this calculation for the remaining time intervals:
t=15 minutes:
VKMnO4 = 19.6 mL
Moles of KMnO4 used = 0.0196 L x [KMnO4] moles/L
Moles of H2O2 = Moles of KMnO4 used x (3 moles H2O2 / 2 moles KMnO4)
t=25 minutes:
VKMnO4 = 12.3 mL
Moles of KMnO4 used = 0.0123 L x [KMnO4] moles/L
Moles of H2O2 = Moles of KMnO4 used x (3 moles H2O2 / 2 moles KMnO4)
t=45 minutes:
VKMnO4 = 5.0 mL
Moles of KMnO4 used = 0.005 L x [KMnO4] moles/L
Moles of H2O2 = Moles of KMnO4 used x (3 moles H2O2 / 2 moles KMnO4)
Now, plot the concentration of H2O2 against time on a graph. In this case, the concentration of H2O2 is represented by the number of moles of H2O2 divided by the volume of the sample solution used.
t (mins) Concentration of H2O2 (moles/L)
0 moles (calculated)
5 moles (calculated)
15 moles (calculated)
25 moles (calculated)
45 moles (calculated)
If the graph of concentration vs. time is a straight line with a negative slope, it indicates that the reaction is a first-order reaction.