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Is it correct that if you alter the proportions of the reactants of many chemical reactions, especially step-wise, the products will change?

Here is an example, please tell me if it is right or not: \begin{align} \ce{KOH + H2SO4 &-> KHSO4 + H2O}\\ \ce{2KOH + H2SO4 &-> K2SO4 + 2H2O} \end{align}

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    $\begingroup$ Just because you can write a different chemical reaction given different stoichiometric numbers does not mean it is more (or less) likely to occur if you provide a different concentration of the reagent(s). I could write the a completely ridiculous - but balanced - chemical equation. It doesn't mean it will ever happen. If you wish to know more about which reaction will predominantly occur, you need to know more information about the thermochemistry and kinetics! $\endgroup$ – Argon Jul 23 '17 at 3:22
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Chemistry is much more complicated than just writing balanced chemical equations. In your case, the reaction is in equilibrium. It would be all much clearer if you took a couple classes of general chemistry.

But if you really want a clear cut answer: since this is an acid-base neutralisation, you would be right. With one equivalent of $\ce{KOH}$, you would find mainly $\ce{KHSO4}$ (with traces of $\ce{KOH}$, $\ce{H2SO4}$ and $\ce{K2SO4}$, which would be mainly dissociated ions anyway.) By adding more, you would shift the equilibrium toward $\ce{K2SO4}$.

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