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I know that for group 13 metals in the p block, the stability of +1 OS is generally more than the stability of +3 OS as it is energetically not favourable to attain the higher OS of +3 and such ions act as strong oxidising agents. $$\ce{\overset{+3}{Tl}+2e^-->\overset{+1}{Tl}}$$ This is called the inert-pair effect. Today, however, I learned in group 13 of p-block metals that the metals in +1 OS are more ionic than those in +3 OS for the same metal. Why is metal in its lower OS of +1 more ionic but in its higher OS of +3 more covalent? For example, Thallium(I) chloride $\ce{TlCl}$ (in its +1 OS) is more ionic or less covalent, and Thallium(III) chloride $\ce{TlCl3}$ (in its +3 OS) is more covalent or less ionic. Does this also suggest that ionic is more stable than covalent in this situation?

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It can be explained by fajans' rules. As the positive charge on an atom increases its size decreases as a result polarising power increases. If polarising power increases then it distorts the electron cloud towards itself and hence ionic nature of the bond decreases.
This is the reason why Thallium(I) chloride is more ionic than Thallium(III) chloride.

Does this also suggest that ionic is more stable than covalent in this situation?


It may not be. Because you can't say that ionic is more stable than covalent. For example, consider diamond which is the one of the hardest substance known to us which is a giant covalent polymer. The actual reason for the stability of Tl(I) over Tl(III) is inert pair effect and it is what you have texted first.

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There is another effect : relativity. In the 6th line of the periodic table (containing $\ce{Tl}$), relativity effect becomes important. Even though electrons have no velocity, their behavior does change as if outer electrons were moving at nearly the velocity of light. This was shown by Pekka Pyyko, Accounts of Chemical Research, Vol.$12$, No. $8, 1979$, p. $276 - 281$.

As a consequence, electrons of the outer shells are so fast that their dimensions decrease, so that they are "absorbed" by the other inner shells. Their chemical properties look like atoms having "lost" $26$ electrons and protons. This is why Thallium ($Z = 81$) is chemically similar to $\ce{Cs}$ $(Z = 55 = 81 - 26)$: both form soluble and stable $\ce{M^{+}}$ ions.

For the same reason, its neighbours have properties which are also changed in the same way. On its right, lead ($Z = 82$) looks like baryum ($Z = 56 = 82 - 26$), as both $\ce{PbSO4}$ and $\ce{BaSO4}$ are insoluble compounds. On its left, mercury ($Z = 80$} is "nearly" a noble gas like xenon ($Z = 54 = 80 - 26$) : it is liquid, boiling at low temperature ($356°C)$ : so it is "nearly" a gas, at least with respect to its neighbors, boiling at $1457°C˙ (\ce{Tl})$, and $2600°C˙(\ce{Au})$. On the other hand, mercury is chemically unique : it is the only metal producing an ionic dimer in aqueous solution : the cation $\ce{Hg2^{2+}}$. This property is also known for noble gases, which may produce ions like $\ce{He2^{+}}$ in special circumstances. And left to left, gold ($Z = 79$) is "nearly" a halogen : it looks a little bit like iodine ($Z = 53 = 79 - 26$), as it produces an ionic compound with cesium : $\ce{CsAu}$.

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    $\begingroup$ Mercury is not the only metal to produce a dimeric ion in the +1 oxidation state. Zinc, cadmium, and even the alkaline earth metals beryllium, magnesium and calcium have been caught doing the same thing. Mercurous ion is, however, the most common case. $\endgroup$ Dec 26, 2021 at 23:09

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