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What is the rate expression for decomposition of $\ce{H2O2}$ in the presence of a catalyst?

As far as I know for catalase, it is like this: $$\ce{Rate = k[H2O2][Catalase]}$$

I don't know what it is for the catalysts $\ce{MnO2}$ and $\ce{Fe2O3}$. Another question in my mind is that even if it's similar to that of catalase, since these are powdered and so do not have a concentration, how can I express it?

It is kind of emergency so any help would be greatly appreciated.

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

I found on web that both reactions are probably (still not sure even though I saw it) first order reactions.

Edit: Is it possible that there shouldn't be anything to be added and it will only affect the $\mathrm{k}$?

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    $\begingroup$ Don't use MathJax or LaTeX in tiles. Don't use \ce{} for rate constants, use \mathrm{} instead. $\endgroup$ – Zenix Apr 15 at 23:38
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For catalase, it is most likely Michaelis-Menten kinetics.enter image description here

At typically low enzyme concentration, this would be first order in catalase. For hydrogen peroxide, it is first order at low concentrations (<< Km) and approaches zero order at high concentration (>> Km). This behavior is also called saturation kinetics.

I don't know what it is for the catalysts $\ce{MnO2}$ and $\ce{Fe2O3}$. Another question in my mind is that even if it's similar to that of catalase, since these are powdered and so do not have a concentration, how can I express it?

For catalysts in the solid phase, it is the surface area (compared to the volume of the solution) that matters. You might see similar saturation kinetics, indicating that at some concentration of reactant, all the surface area is used so that an increase in reactant concentration no longer translates into an increase in rate.

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  • $\begingroup$ So can we say that its effect can be seen as a change in rate constant? $\endgroup$ – Mathrix Apr 16 at 15:45
  • $\begingroup$ If the amount of catalyst is always the same, you could define an effective rate constant that incorporates information about the catalyst (like giving distinct rate constants for different solvents or pH values instead of including the hydrogen ion concentration explicitly in the rate equation). However, often we use the rate expression to learn about the mechanism, and then it would be counterproductive. $\endgroup$ – Karsten Theis Apr 16 at 16:14

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