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Which of the following has the highest molar conductivity?

(A) Diaminedichloroplatinum(I)
(B) Tetraamminedichlorocobalt(III) chloride
(C) Potassium hexacyanoferrate(II)
(D) Hexaaquochromium(II) bromide

Since mobility depends on the size, charge and the number of particles, how can we determine the extent of molar conductivity from the given data?

The solution provided to me considered only the number of ions that each gives. But is this justified? Because they all have different sizes, charges and thus different mobility.

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Charge transport depends on the presence of charge carriers, and an increase of the concentration of charge carriers may increase the electric conductivity. This is the basis of the answer given to you which (implicitly) assumes each of these complexes dissociate, e.g.

$\ce{K4[Fe(CN)6] <=> 4 K+ + [Fe(CN)6]^{4-}}$

in your solvent completely. In this view, charge transport happenz without moving these carriers on a macroscopic level (like the salt bridge used to connect electrochemical cells). You may imagine a bucket brigade, instead people exchanging buckets of water, ions shuttle electrons.

On the other hand, there are examples where charge transport is coupled to the transport of matter (e.g., ions) on a macroscopic scale. Proteins and nucleic acids, for example, may be separated by this (e.g., gel electrophoresis); their different size (and shape, and charge) quite noticeably influence how quickly they travel in an electric field.

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