There are main ideas of the kinetic molecular theory of gases. First is that pressure of gases is an expression of an average force that modifies the total momentum of molecules striking the wall. the second idea is that the temperature of a gas is an expression of the average kinetic energy of its molecules.
This second idea can be applied also for liquids:
`C*T =(m*v^2)/2` where `C` is a constant (1)
When liquids boil the velocity of liquid's molecules overcome the interaction intermolecular forces and thus the molecules break free into the gas state. Assuming that both in water and in liquid mercury the strength of these intermolecular forces is about the same, one can deduce that about the same average velocity of their molecules will be needed at the boiling point:
But since the mass of one H20 molecule is 2+16 =18 amu (atomic mass units) and the atomic mass of Hg is 200 amu, this implies that the average kinetic energy of water is less than the average kinetic energy of mercury.
`m_("H2O")<m_("Hg") rArr (m_("H2O")v_("H2O")^2)/2 < (m_("Hg")v_("Hg")^2)/2`
From this observation and (1) one can imply that at the boiling point:
`T_(H2O) < T_(Hg)`