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Although polarizability and polarizing power sound similar, they are very different indeed and only share one relation: they are both related to the covalent character of ionic bonds, which means that the electrons slightly shared as opposed to being separated. Polarizing power is used to describe cations, which pull electrons away from the anions. Smaller, more positive cations would pull electrons more strongly, so they have more polarizing power. In contrast, polarizability is the ability to pull those electrons towards the anion. If it is a small anion and has a large negative charge, it can more closely hold on to the electron density and would not be polarizable. Hope this helps!
Polarizability is the ability for a molecule to be polarized (have its electron cloud distorted by the pull of the smaller atom, and it increases as the volume occupied by electrons increases. Whereas polarization power is the ability of a cation to distort an anion. If the degree of polarization is quite small, an ionic bond is formed, while if the degree of polarization is large, a covalent bond is formed.
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