I'm specifically talking about the decomposition of hydrogen peroxide by bovine catalase. The number of catalase molecule obviously doesn't change, so there's the same number of catalase molecule within an undiluted and a diluted solution. Also, seeing as water is not an enzyme inhibitor, and doesn't change the pH or temperature, then shouldn't the rate of reaction remain the same regardless of concentration, since every environmental conditions & the number of catalase molecule in the solution before dilution is the same after it is diluted?
[…] there's the same number of catalase molecule within an undiluted and a diluted solution. Also, seeing as water is not an enzyme inhibitor, […]
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You are right in that the absolute amount of catalase molecules does not change upon dilution, but the concentration does!
Reactions are about collisions of the reactants and in the case of dilutions, there are more collisions with innocent bystanders than with an other reactant.
If you diluted the catalase, while keeping the peroxide concentration fixed (by adding both water and peroxide to the solution), then you're right, the total reaction rate (measured in reactions catalyzed per second, within the whole solution) would not change.
However, by adding just water to the solution, you're diluting both the enzyme and the peroxide. The lower the peroxide concentration is, the longer it takes for each catalase enzyme unit to bump into another peroxide molecule after reacting with the previous one.