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Question

Which of the following complex has lowest molar conductivity?

  1. $\ce{[Co(NH3)6][Cr(NO2)6]}$
  2. $\ce{[Cr(NH3)5(NO2)][Co(NH3)(NO2)5]}$
  3. $\ce{[Cr(NH3)4(NO2)2][Co(NH3)2(NO2)4]}$
  4. $\ce{[Co(NH3)5(NO2)][Cr(NH3)(NO2)5]}$

Answer

3. $\ce{[Cr(NH3)4(NO2)2][Co(NH3)2(NO2)4]}$

My approach

My textbook only has examples of single centered complex ions, unlike what seems to be coordination isomers in the question. Normally, I see stuff with hydrates and ammine ligands which we predict by the number of active anions in the primary valency. But I have no clue on how to proceed with this question and the website does not provide any solution/ reference.

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    $\begingroup$ Hint: Check the ion charges. $\endgroup$ – Poutnik Sep 3 '20 at 19:35
  • $\begingroup$ Assuming NO2 to contribute -ve 1 charge, I can see that the third option is +1 -1 coordination in primary valency, while others have higher charges. So since this particular compound having the least charge separation it should have the least molar conductivity, is my logic right? $\endgroup$ – madhavpcm Sep 3 '20 at 19:53
  • $\begingroup$ If there are ions A+ and B++ of about same size in the same electrostatic field, which would move faster ? Is conductivity proportional to mobility and charge ? $\endgroup$ – Poutnik Sep 4 '20 at 4:24
  • $\begingroup$ B++, since it is conductivity is proportional to charge, but I think hydration effects and charge/mass ratio is also involved. $\endgroup$ – madhavpcm Sep 4 '20 at 5:00
  • $\begingroup$ They are minor to the charge effect, that is higher than proportional. As the ion is faster AND carries bigger charge. $\endgroup$ – Poutnik Sep 4 '20 at 6:43

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