In the following reaction won't the sulphuric acid dehydrate the secondary alcohol after it's formed?

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It could, but the addition of water would push equilibrium toward the hydrated product, and the $\ce{H2SO4}$ would likely transfer into the water layer that you made by adding $\ce{H2O}$.

Plus, you would only make stoichiometric sulfuric acid. Depending on the amount of water, the pH of the solution formed could be fairly neutral. Also, usually, the acid (despite being a catalyst) is used in large excess for dehydration reactions.

Therefore, it is possible (given the right conditions) but unlikely.

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