The Lennard-Jones potential energy, U(x), is a function of \"x\"the distance between a pair of molecules. It is frequently calledthe van der Walls potential between molecules for dipole-dipoleinteractions. The potential is
U(x) = C12/ x^12 -C6/x^6Â Â Â Â Â Â Â Â Â Â Â Â [1]
Here we assume for water molecules:
C12 = 9.5 x 104\" J•m12
C6 = 1 x 10-76 J•m6.
(a) What is the separation distance (Xs) between two watermolecules where the applied force (F) to pull the molecules apartis a maximum. Recall F = dU/dx.
(b) Calculate the maximum force (Fmax) required to separate twowater molecules [overcome the cohesive force between themolecules].
(c) If oxygen has a mass of 16 g/mole and hydrogen has a mass of1 g/mole, using Avodadro's number (6 x 10^23 molecules/mole) andthe gravitational force of 9.8 m/s^2, calculate the force ofattraction (due to weight) of one water molecule toward Earth.
(d) How does the gravitational force compare to van der Waalsforce of attraction of two water molecules?
