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What is the rate equation of this reaction with the presence of catalysts $\ce{MnO2}$, $\ce{PbO2}$ and $\ce{Fe2O3}$? (asking for each of them, separately, not altogether)

$$\ce{2H2O2 -> 2H2O + O2}$$

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  • $\begingroup$ TL, DR: There's no equation. $\endgroup$ – Mithoron Dec 24 '19 at 20:39
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The rate of the reaction between a solute and a solid catalyst cannot be defined in the usual way, namely with an expression which is proportional to the concentration of the catalyst. Such a rate is proportional to the surface of the catalyst. And the surface of a powder is a parameter difficult to know with precision

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    $\begingroup$ How can I find it? I am working on experiments that show the difference at $\ce{E_a}$ between two different catalysts. In order to do this, do I not need the rate equation to find the value of $\ce{k}$, so that I can use Arrhenius equation? What can/should I do? $\endgroup$ – Mathrix Dec 23 '19 at 21:50
  • $\begingroup$ For particular dosing of the catalyst, measure the rate for various temperatures and H2O2 concentration. You can then get both factors for Arrhenius equation and reaction order for H2O2. $\endgroup$ – Poutnik Dec 24 '19 at 13:33
  • $\begingroup$ @Poutnik. Even if you choose the same amount of catalyst and H2O2, the rate of reaction depends on the dimension of the grains. The reaction goes quicker with fine grains than with coarse grains. $\endgroup$ – Maurice Dec 24 '19 at 13:56
  • $\begingroup$ @Maurice sure, but I have meant the same catalyst lot. By other words, keeping constant as many degrees of freedom as possible, varying just [H2O2] ( the reaction order ) or temperature ( Arrhenius eq. parameters ). $\endgroup$ – Poutnik Dec 24 '19 at 16:38
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The decomposition of H2O2 is complex and has been the source of several studies.

On iron oxide surface, here is a cited work `Catalytic Decomposition of Hydrogen Peroxide on Iron Oxide: Kinetics, Mechanism, and Implications’. Some selected quotes:

"As depicted in Figure 2, the decomposition rate of H2O2 appears to be independent of the goethite particle size. On the other hand, the decomposition rate is directly proportional to the iron oxide concentration (Figure 3)."

Also: "The large surface area measured for the granular particles is equivalent to the external surface area of the colloidal particles, as reported in the literature. This might explain the observed lack of size effect in the present study....

However, the experimental results showed that the observed kinetics and rate constants were not affected by various concentrations of H2O2, and the dissolved iron concentration was always low (e0.2 mg/L)."

Table 2 and Table 3 outlined the reaction mechanism.

I would expect similar results with H2O2 for other transition metal oxides, but MnO2 is claimed to avoid a radical based path (per Wikipedia), and the decomposition reaction can be energetic (and possibly explosive with 30% H2O2 in a closed vessel).

Here is another example at "Active sites and mechanisms for H2O2 decomposition over Pd catalysts". Some extracts:

"We conclude that both Pd(111) and OH-partially covered Pd(100) surfaces represent the nature of the active site for H2O2 decomposition on the supported Pd catalyst reasonably well. Furthermore, all reaction flux in the closed catalytic cycle is predicted to flow through an O–O bond scission step in either H2O2 or OOH, followed by rapid H-transfer steps to produce the H2O and O2 products. The barrier for O–O bond scission is sensitive to Pd surface structure and is concluded to be the central parameter governing H2O2 decomposition activity."

Also:

"A mean-field microkinetic model was developed to describe the experimentally measured reaction rates, reaction orders, and apparent activation barrier."

And:

"The decomposition of H2O2 has been studied both in the vapor phase (47) and aqueous phase (48) (thermal, noncatalyzed), and over a variety of materials including metal oxides (49⇓–51) and metal ions in solution (52, 53). Based on these studies, we have compiled an encompassing network of 17 elementary reactions involving four closed-shell species (H2O2, H2O, O2, H2) and four surface intermediates (O, H, OH, OOH), which are shown in Table 1. Elementary reactions are classified as follows: adsorption/desorption, O–O bond scission, dehydrogenation, and hydrogen transfer."

Also:

"The microkinetic modeling results suggest that both the close-packed Pd(111) and more open Pd(100) facets can contribute to the total H2O2 decomposition activity. Furthermore, on both Pd facets, all reaction flux is predicted to go through an O–O bond breaking step (in either H2O2* or OOH*), followed by successive H-transfer steps to O*/OH* adsorbates. The relevant surface coverage of O*/OH* is then a function of the ability of the Pd surfaces to generate the O*/OH* fragments through O–O bond breaking [which can vary strongly with surface coverage, as seen from calculations on the OH*-modified Pd(100)], and the availability of H-donating species (H2O2* and OOH*) to reduce O*/OH* to H2O* through the rapid H-transfer reactions."

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