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Mp an Bp are mainly determined by the G-T curves of the solid and the liquid phases.
If you plot the G-T curve for the solid phase and the liquid phase simultaneously on the same plot, then at a particular temperature only one curve will be lower than the other and that particular phase will be stable. At the particular temperature where the liquid curve becomes lower than the solid curve, melting occurs and that is the melting point. Similarly for boiling point.
The slopes of the G-T curves are controlled by many factors, the chief amongst them being pressure and entropy.
Other factors can indirectly contribute to this, and in some special cases become the dominating factor in reduction or elevation of mp, bp. However, behind the scenes, it is the G-T curves that determine everything, for any factor that affects bp or mp (H-bonding, dipole interactions etc, ), all effectively modify the G-T curve accordingly.
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