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Why does sulfur dichloride have a lower boiling point than phosphorus trichloride? Is it to do with the higher number of electrons causing stronger id-id interactions in PCl3, or do we need to compare pd-pd interactions also?

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I think you're looking down the wrong path to explain this. Boiling point can often be explained by looking at the interactions between molecules such as hydrogen bonding, dipole-dipole interactions, and london forces, as well as overall molecular mass. I would explain this phenomenon by looking at two data points for each molecule. The dipole of $\ce{SCl2}$ is 0.4 Debye and the dipole of $\ce{PCl3}$ is approximately 0.780 Debye.$\ce{^{1,2}}$ Based on this alone, I would expect $\ce{PCl3}$ to have a higher boiling point. If you also look at the mass of each molecule, 102.97 g/mol for $\ce{SCl2}$ and 137.33 g/mol $\ce{PCl3}$, it becomes pretty clear which substance one should predict to have the higher boiling point. It's $\ce{PCl3}$.

Ref 1. http://openmopac.net/PM7_accuracy/data_molecules/sulfur%20dichloride_jmol.html

Ref 2. https://cccbdb.nist.gov/diplistx.asp

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