Boltzmann's formula for the work to separate molecules when a liquid turns into a gas, energy is required to separate the liquid molecules that are "locked together" by attractive forces. energy is also required to push back the atmosphere to make room for the expanding vapor. in short, work must be done to overcome internal and external forces. in his monumental lectures on gas theory, ludwig boltzmann derived a delightful lite formula for the work required to separate liquid molecules based on van der waal's writes if one neglects the density of the vapor compared to that of the liquid, then is the work of separation of the liquid particles". in this formula, wis the work per mole, a is the interaction constant in van der waals theory, and rho is the density of the liquid (expressed as moles per liter). (a) derive boltzmann's formula. (b) use this formula to calculate the numerical value of w for water (a-554 j l/mo mercury (a 820 j/mol) and (c) express your values of w in natural atomic units: ev per molecule. in these units, w is an atomic parameter: the strength of a molecular bond, i. e. the energy required to break the bond or the depth of the potential well representing the interaction between two molecul avera - and compare it to your calculated value of the energy of the h, o-h, o bond that holds two water molecules together. es. look up the ge energy of an h-o bond -the bond that holds two atoms together in one water molecule (d) calculate the latent heat of vaporization l for water and mercury at their standard boiling points. use the w formula for the internal work. for the external work, assume the vapor obeys the ideal gas law. compare your theoretical estimates for l with the experimental values. boltzmann was well aware that van der waal's theory is an approximate theory of liquids and a is an empirical constant. although an approximation to reality, boltzmann's w formula provides both simple and deep insight into the relation between heat (l) and atoms (a).