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I'm a high school student researching the conductivity of electrolyte solutions. In this excerpt of the CRC Handbook, I noticed that different ions containing chlorine have different limiting molar conductivity, and there seems to be a trend between molar conductivity and the oxidation state of chlorine:

Ion Oxidation state of chlorine $\Lambda$ in $\pu{e-4 m2 S mol-1}$
$\ce{ClO2-}$ +3 52
$\ce{ClO3-}$ +5 64.6
$\ce{ClO4-}$ +7 67.3

Does the trend really exist? If so, why did it happen? I found previous researches on the conductivity of $\ce{Fe^2+}$ and $\ce{Fe^3+}$, and the difference seemed to be a result of electrons spinning.

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  • $\begingroup$ It is the similar effect as for molar condutivity of alkali metals. $\endgroup$
    – Poutnik
    Mar 11 at 15:43
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It is the similar effect as for molar conductivity of cations of alkali metals, which grows from $\ce{Li+}$ toward $\ce{Cs+}$, in spite of increasing ionic radius.

The point is, the effective radius of the hydrated ions has the opposite trend as the "naked" ion radius trend. $\ce{Li+}$ ion with the smallest radius has the strongest electrostatic field and the largest hydration sphere and has therefore the lowest molar conductivity.

The similar effect I expect for chlorine oxyacid anions. In this case, there is also decreasing degree of delocalization of the negative charge in trend $\ce{ClO4-} \gt \ce{ClO3-} \gt \ce{ClO2-}$.

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OP is questioning whether there is a trend between oxidation state of center atom and molar conductivity of relevant anion ($\ce{ClO_x^-}$), but gives only three examples. Since given molar conductivity values are from an acceptable source, the trend seems to exist. However, we cannot conclude that it is due to oxidation state of center atom of $\ce{ClO_x^-}$, which are +3, +5, and +7 when $x$ is 2, 3, and 4, respectively. If similar trend is shown by both or either of $\ce{BrO_x^-}$ and $\ce{IO_x^-}$, there is some extra data to consider. Unfortunately, I cannot find the relevant molar conductivity values for these anions.

Nonetheless, I agree with Poutnik that this may be the similar effect as for molar conductivity of cations of alkali metals. In that answer, Poutnik has discussed that the trend is probably caused by the increasing ionic radius. When I was looking for ionic radii of corresponding anions, I found this reference (Ref.1), which described the bond lengths of $\ce{X-O}$ of $\ce{ClO_x^-}$, $\ce{BrO_x^-}$, and $\ce{IO_x^-}$. Out of curiosity, I checked a trend between bond lengths of $\ce{X-O}$ and molar conductivity:

$$ \begin{array}{c|c|c|c} \text{Oxyhalo anion} & \ce{X-O}\text{ bond length, pm} & \text{molar conductivity, }\Lambda & \Lambda^2 \\ \hline \ce{ClO2-} & 159.1 & 62 & 3844 \\ \ce{ClO3-} & 150.1 & 64.6 & 4173 \\ \ce{ClO4-} & 145.3 & 67.3 & 4529 \\ \ce{BrO3-} & 167.1 & 55.7 & 3102 \\ \ce{IO3-} & 182.9 & 40.5 & 1640 \\ \hline \end{array} $$

The plot of $\ce{X-O}$ versus $\Lambda^2$ is a straight line with good agreement ($R^2 = 0.9769$):

Plot of X-O vs lambda^2

I included the data of $\ce{BrO_3^-}$ and $\ce{IO_3^-}$ for better representation. Unfortunately we don't have other $\ce{BrO_x^-}$ and $\ce{IO_x^-}$ conductivity data. Still, good relationship with five data point is better than three. What I'm saying is it is close to zero chance that to find direct or indirect relationship of molar conductivity versus oxidation state of the center atom as OP is wondering. Yet, there is a good chance to have a relationship between molar conductivity versus $\ce{X-O}$ bond length as depicted in the image. I do not know why is that but it is worth noting.

References:

  1. Lars Eklund, Tomas S. Hofer, Ingmar Persson, "Structure and water exchange dynamics of hydrated oxo halo ions in aqueous solution using QMCF MD simulation, large angle X-ray scattering and EXAFS," Dalton Trans. 2015, 44(4), 1816–1828 (doi: 10.1039/c4dt02580f).
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