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I know that the limiting current is proportional to the square root of the rotation speed, but what does the slope of the plot represent?

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if you mean the following plot: enter image description here

(Electrochemical Methods. fundamentals and applications, p. 341).

If a bulk concentration is the same as the concentration at the surface of the electrode (the mass-transfer is very high) than the current will be independent on $\sqrt\omega$ and will be constant at the value $i_K$.

The slope of the bold line represent deviation form Levich line and tend towards the limit $\lim_{\sqrt\omega \to \infty} i = i_K $. The higher the speed of rotation is, the less is the electrode reaction limited by mass-transfer effects.

The Levich line (dashed; $\frac{i}{\sqrt\omega}$ ) is constant only when $i_K$ is much larger.

enter image description here

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