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The inductive effect is the effect on electron density in one portion of a molecule due to electron-withdrawing or electron-donating groups elsewhere in the molecule. This has to do with differences in electronegativity between atoms in a molecule. In a covalent bond between two atoms of unequal electronegativity, the atom with higher electronegativity withdraws electron density towards itself.
The inductive effect can be useful in determining relative acid strength because if there are acids in which the same type of bond is broken when donating the H atom, then the acid that results in the most stable anion is the strongest acid. For example, when comparing CLOH and IOH, the O-H bond is broken in both cases, so the stability of the resulting anions must be considered when determining the stronger acids. Since Cl is more electronegative than I, it will withdraw electron density from the O in the Cl-O bond than the I in the I-O bond. This withdrawing of electron density (the inductive effect) causes the Cl-O bond to be more stable than the I-O bond because the electron density is more spread out, thus stablizing the molecule. Since the ClO anion is more stable than the IO anion, ClOH is the stronger acid.
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