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Both $\ce{PCl3}$ and $\ce{SCl2}$ are $\mathrm{sp^3}$ hybrid. $\ce{PCl3}$ has 1 lone pair whereas $\ce{SCl2}$ has 2 lone pairs, so due to more lp-lp repulsion, $\ce{SCl2}$ should have smaller bond angle than $\ce{PCl3}$. But practically, $\ce{SCl2}$ has got larger bond angle than $\ce{PCl3}$. Why is it so?

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You are worried about 3pm here. Possibly the slightly shorter bond causes slightly more repulsion between the electrons on the chlorines. There doesn't seem to be enough difference to be concerned about changes in hybridization. Personally I think simple use of hybrid orbitals and realization that unpaired electrons occupy such orbitals and take up space goes a long way towards understanding simple molecular structure.

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