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We say that the overall rate doesnt increase if we increase the concentration of a reactant in a non rate determining step. Does that mean that the speed of that non rate determining step increase but at the same time something happens to counter the increase in speed? Because it doesnt make sense to say that the speed doesnt increase with increase in concentration.

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Let's think about this reaction:

$\ce{ A + B->[k_1][] C + D ->[k_2][] E }$

let's say $k_1 << k_2$ so the first reaction is much, much slower than the second step (at equal concentrations)

Now it get's a little bit tricky since the reaction rates depend on the concentration. Let's assume for now that the concentrations of $A$, $B$ and $D$ are in a way that the reaction rate of the first step is really much faster than the second step.

What happens is that $A$ and $B$ react to $C$ quite slowly, but once you got any $C$ it reacts very fast with $D$ to $E$. This means your concentration of $C$ will always be quite low, since everything that is produced will react to $E$. But this also means that the concentration of $E$ is basically increasing with the rate of the first step. The slow reaction part is limiting the overall rate.

What happens if we increase the concentration of $D$? Well, the second step will be even faster, so all the $C$ that comes out of the first step will be converted to $E$ even faster. But the first step is still slow, so your $E$ concentration will still increse approximately with the rate of the first step.

Only if we would reduce the concentration of $D$ to very low levels (much lower than $A$ and $B$) we would see a difference, in that case the second reaction will get slower than the first one (reaction rate depends on concentration) and will be the limiting step.

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