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Consider the following reaction:

$$\ce{CaC2 + 2H2O -> Ca(OH)2 + 2C_{2}H_{2}}$$

If it can be considered as an acid-base reaction, is it a Brønsted-Lowry (B.L.) reaction or a Lewis reaction?

If it is B.L., of course it is also Lewis; but I cannot understand if it can be B.L. in this case, since 2 protons are actually passed to the double carbon atom, but there is also the $\ce{Ca}$.

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    $\begingroup$ Please don't use MathJax in the title field in the future. Also, you might want to read up on using the mhchem LaTex package :-) $\endgroup$ – paracetamol Jan 4 '18 at 19:46
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We may regard the calcium hydroxide and calcium carbide as essentially ionic except for the covalent bonding within the anions. So there is no Lewis reaction involving the calcium.

That leaves the proton transfer, which can be described fully by the B-L theory. You actually have two reactions, successively forming $\ce{C2H-}$ and then $\ce{C2H2}$.

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    $\begingroup$ I think it would be better to say that one can ignore Lewis aspect of this reaction, then that it lacks one. $\endgroup$ – Mithoron Jan 4 '18 at 21:51

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