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I recently came across a question in which an option is 'Breaking a chemical bond is the first step in any chemical reaction', which lead me to think of reactions which do not involve bond breaking. The only reaction I can think of is dimer formation, but a Google search reveals no more. Surely this cannot be the only example?

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The reaction of a Lewis acid with a Lewis base results only in bond formation. Your question gets at the essence of chemistry, though. A chemical reaction is the rearrangement of electrons between atoms. So generally, most reactions will involve breaking bonds. Even for monomers (e.g. alkenes) to polymerize, $\pi$-bonds within the monomers have to be broken to form $\sigma$-bonds in the polymer. You seldom have one without the other.

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    $\begingroup$ Electron transfer is such an example; $\ce{D + A \to D^+ = A^-}$. $\endgroup$ – porphyrin Jul 28 '18 at 6:53
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Precipitation reactions? If you will grant me that an aqueous ion is free. (But maybe you don't and consider the solvated ion bonded to nearby water.)

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