Reaction of Potassium Permanganate and Hydrogen Peroxide solution

[neilparker62]

TL;DR Summary

Reaction Rate experiment

With the peroxide solution in excess, we added 10ml vinegar and 10ml of different concentrations of permanganate and timed the reaction. The basics are that the more concentrated the permanganate , the faster the reaction. I would just like to know what the theoretical relationship is between reaction rate (or time to completion) vs concentration ?

 

[TeethWhitener]

You happened to choose a very complicated reaction (paywalled Inorg. Chem. article):
https://pubs.acs.org/doi/pdfplus/10.1021/ic00224a030
Typically, for elementary reactions (where the stoichiometry reflects the reaction mechanism faithfully), reactions are either unimolecular, in which case the rate is linear in the concentration, or bimolecular, in which case the rate is quadratic. (NB--higher order elementary reactions are exceedingly rare, a reflection of the fact that correctly-oriented triple (or more) collisions of molecules are exceedingly rare.)

In the case of permanganate reacting with hydrogen peroxide:
$$2MnO_4^-+5H_2O_2+6H^+\rightarrow2Mn^{2+}+5O_2+8H_2O$$
the stoichiometry does not reflect the reaction mechanism faithfully.

The article above states that the reaction proceeds in three phases: 1) a fast initial phase which is roughly bimolecular ($Rate \propto [MnO_4^-][H_2O_2]$), 2) a slow induction phase that sees a buildup of $Mn^{2+}$, and 3) an autocatalytic phase, where the manganous ion catalyzes the reduction of the permanganate via a hypothesized Mn(III) pathway, producing more manganous ion, etc., etc. The article goes into much more detail than this, but suffice it to say that the answer to your question isn't straightforward.

 

[Borek]

Even balancing this reaction isn't easy. Check that

2KMnO₄ + H₂O₂ + 3H₂SO₄ → 3O₂ + 2MnSO₄ + K₂SO₄ + 4H₂O

is correctly balanced as well (even if it doesn't reflect the observed stoichiometry).

 

[neilparker62]

You happened to choose a very complicated reaction (paywalled Inorg. Chem. article):
https://pubs.acs.org/doi/pdfplus/10.1021/ic00224a030
Typically, for elementary reactions (where the stoichiometry reflects the reaction mechanism faithfully), reactions are either unimolecular, in which case the rate is linear in the concentration, or bimolecular, in which case the rate is quadratic. (NB--higher order elementary reactions are exceedingly rare, a reflection of the fact that correctly-oriented triple (or more) collisions of molecules are exceedingly rare.)

In the case of permanganate reacting with hydrogen peroxide:
$$2MnO_4^-+5H_2O_2+6H^+\rightarrow2Mn^{2+}+5O_2+8H_2O$$
the stoichiometry does not reflect the reaction mechanism faithfully.

The article above states that the reaction proceeds in three phases: 1) a fast initial phase which is roughly bimolecular ($Rate \propto [MnO_4^-][H_2O_2]$), 2) a slow induction phase that sees a buildup of $Mn^{2+}$, and 3) an autocatalytic phase, where the manganous ion catalyzes the reduction of the permanganate via a hypothesized Mn(III) pathway, producing more manganous ion, etc., etc. The article goes into much more detail than this, but suffice it to say that the answer to your question isn't straightforward.

Would there be any simplification given one maintains as constant the concentration of peroxide and of vinegar as well as the volume of the reaction mixture (30ml) ? Also use quite dilute permanganate (< 1g/litre). For a school level experiment you get quite convincing time differences depending on the dilution of the 10ml permanganate - my 'rough and ready' results do seem to indicate quite a good linear relationship: concentration vs 1/t. It goes a bit 'pear-shaped' at higher concentrations.

For the record we are using 10ml of 1% peroxide, 10ml of vinegar and the 'stock solution' of permanganate is about 6.4 g/litre. Diluted > x2.

 

[TeethWhitener]

Certainly if the permanganate is dilute enough, it might all get used up before the necessary complexes build up to a level where autocatalysis starts to become a significant factor.

And yes, the proper course of action is to keep as many of the reagents at as constant a concentration as possible in order to accurately assess kinetics. This can be tough to do if you’re adding multiple solutions together (since adding one solution dilutes the other solution).

 

[neilparker62]

Certainly if the permanganate is dilute enough, it might all get used up before the necessary complexes build up to a level where autocatalysis starts to become a significant factor.

And yes, the proper course of action is to keep as many of the reagents at as constant a concentration as possible in order to accurately assess kinetics. This can be tough to do if you’re adding multiple solutions together (since adding one solution dilutes the other solution).

The concentration formula is essentially grams or moles/volume. So as not to change either peroxide or acid concentration the experiment used 10ml peroxide , 10 ml vinegar and 10 ml of various concentrations of Permanganate. That is the experiment was carried out at constant volume.

If we rather decided to keep the numerator of moles/volume constant for all reactants, what result would we expect ? So in essence we have a 'stock' reaction with a set number of moles of reagent(s) which do not change throughout the experiment. All we do is dilute the whole reaction mix. Is there a general formula which relates reaction time to volume and/or dilution factor under the above conditions ?

 

[TeethWhitener]

The concentration formula is essentially grams or moles/volume. So as not to change either peroxide or acid concentration the experiment used 10ml peroxide , 10 ml vinegar and 10 ml of various concentrations of Permanganate. That is the experiment was carried out at constant volume.

This sounds fine. I’m assuming, since this is permanganate and it’s a school experiment, that the basic procedure is 1) mix reagents, 2) monitor the permanganate absorbance using UV-Vis spectrometry. Correct me if I’m wrong.

Is there a general formula which relates reaction time to volume and/or dilution factor under the above conditions ?

The reaction will always depend on concentration, but as I mentioned earlier, the dependence isn’t simple for this reaction. The reaction shouldn’t depend on absolute volume (unless you’re using a container with dimensions comparable to the molecules themselves). Also, keep in mind that (assuming I was right about the procedure) you’re only seeing the portion of the reaction where the purple Mn(VII) color fades. That’s fine, but it just means that you’re not monitoring the concentrations of the other species during the course of the reaction. So if you’re trying to judge the entire reaction from Mn(VII) to Mn(II), you’ll be missing a lot of information about the intermediate steps.

 

[neilparker62]

This sounds fine. I’m assuming, since this is permanganate and it’s a school experiment, that the basic procedure is 1) mix reagents, 2) monitor the permanganate absorbance using UV-Vis spectrometry. Correct me if I’m wrong.

A lot more 'crude' than that. Using a simple syringe, we put 10ml of stock peroxide solution and 10ml of vinegar in a white or colourless plastic cup. Then add 10ml permanganate also from a syringe and start the timer. t=0 is not well defined since you essentially hit 'start' on the stopwatch as soon as the plunger is down on the 10ml syringe. And 'monitoring' is just waiting for the colour change (purple -> clear) to occur - again not always well defined since the purple tends to 'linger longer' as your permanganate solutions become more dilute.

The reaction will always depend on concentration, but as I mentioned earlier, the dependence isn’t simple for this reaction. The reaction shouldn’t depend on absolute volume (unless you’re using a container with dimensions comparable to the molecules themselves). Also, keep in mind that (assuming I was right about the procedure) you’re only seeing the portion of the reaction where the purple Mn(VII) color fades. That’s fine, but it just means that you’re not monitoring the concentrations of the other species during the course of the reaction. So if you’re trying to judge the entire reaction from Mn(VII) to Mn(II), you’ll be missing a lot of information about the intermediate steps.

Appreciate from what you've said that the reaction is complex. But if we keep n moles of all reagents exactly the same, then exactly the same reaction path should occur whatever the dilution. So then the time difference (for different dilution factors) will be due to an increased 'average time' for successful collisions. Well that was my thinking anyway - don't know if it makes any sense ?

 

[TeethWhitener]

Appreciate from what you've said that the reaction is complex. But if we keep n moles of all reagents exactly the same, then exactly the same reaction path should occur whatever the dilution. So then the time difference (for different dilution factors) will be due to an increased 'average time' for successful collisions. Well that was my thinking anyway - don't know if it makes any sense ?

Yes. Once again: reaction rate is dependent on concentration.