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No, chlorine has a lower boiling point than bromine.

Bromine has a boiling point of

332.0 K

(58.8 °C, 137.8 °F)

Chlorine has a boiling point of

239.11 K

(-34.4 °C, -29.27 °F)

I have been assigned a homework assignment to the purpose of explaining why this is, although I have no clue... yet.

The reason for this is that the London Dispersion Force in Bromine is higher than that of Chlorine. London Dispersion Force depends on the polarizability which consists of two parts: number of electrons in each of these two diatomic molecules and the diffuse cloud (which mainly is the size of the molecule). Because Bromine has more electrons than Chlorine (35 to 17) and Bromine is larger than Chlorine (Period 4 > Period 3). Because of the above, Bromine has higher intermolecular force, London Dispersion Force specifically than Chlorine. Thus, it requires more energy to break the bonds between Bromine molecules than Chlorine molecules. In term of thermodynamics, Bromine has higher boiling point than Chlorine.

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