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I'm interested in an aerospace project that requires I know the reaction rate ($[\pu{M/s}]$) of, $$\ce{2 KMnO4 (aq) + 3 H2O2 (aq) -> 3 O2 (g) + 2 MnO2 (s) + 2 KOH (aq) + 2H2O (l)}.$$

I'm just curious if there is an analytic method for finding it?

To that end, I also feel I should double-check. To predict the heat ($[\pu{kJ}]$) released I only need to do the following calculation: $$\Delta H_\mathrm{reaction} = \sum\Delta H_\mathrm{products} - \sum\Delta H_\mathrm{reactants}$$

Is this correct?

My goal is to predict the thrust generated by a hypothetical propulsion system, using this reaction as opposed to combustion.

My thought is if I can derive a theoretical reaction rate then I can calculate a theoretical value for $\mathrm{d}\Delta H_\mathrm{reaction}/\mathrm{d}t$, then thanks to the ideal gas law and thermal physics I should be able to calculate a theoretical max thrust.

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    $\begingroup$ You use mhchem \ce{} by a weird way. You can write $$\ce{KMnO4(aq) + 3 H2O2(aq) -> 3 O2(g) +2 MnO2(s) +2KOH(aq) +2H2O(l)}$$ to get $$\ce{KMnO4(aq) + 3 H2O2(aq) -> 3 O2(g) +2 MnO2(s) +2KOH(aq) +2H2O(l)}$$ Note that phase states are recommended not to be written as subscripts. See chemistry.meta.stackexchange.com/questions/86/… $\endgroup$
    – Poutnik
    Jan 29, 2022 at 0:19
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    $\begingroup$ BTW, it is permanganate, manganate is $\ce{K2MnO4}$. // I doubt the rate can be calculated from basic principles, so unless it is published, it must be measured. TD preference and kinetic rate are independent. $\endgroup$
    – Poutnik
    Jan 29, 2022 at 0:26

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The rate of catalyzed decomposition of H2O2 will depend on the state of division of the catalyst. That will certainly change over the course of the reaction as the MnO2 is formed, then gets reacted upon.

H2O2 has been used since before World War II for propulsion of rockets and torpedoes. https://en.wikipedia.org/wiki/High-test_peroxide

Although it is not stated explicitly in the Wikipedia article, it seems that the rate of decomposition of H2O2 is determined simply by the rate at which it is pumped into the propulsion chamber (with the catalyst separately pumped in). This assumes essentially instantaneous decomposition, which is apparently an adequate approximation.

The reaction of H2O2 with MnO2 or KMnO4 would be similar to hypergolic fuels. The first hypergolic fuel actually used H2O2 along with hydrazine hydrate. "Hypergolically-fueled rocket engines are usually simple and reliable because they need no ignition system. Although larger hypergolic engines in some launch vehicles use turbopumps, most hypergolic engines are pressure-fed." The reaction is said to be spontaneous, but more than that, it is fast, immediate, explosively fast. It is kept from exploding by limiting the amount that gets to react. You could probably call it a limited explosion; the astronauts have essentially declared that their trips are like riding an explosion. https://en.wikipedia.org/wiki/Hypergolic_propellant

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