I know the potential energy due to dispersion interaction for solid argon = -1.4

Question

I know the potential energy due to dispersion interaction for solid argon = -1.40 kJ/mol but I do not know how to calculate the boiling point of argon. Please help!

The intermolecular distance between two closest Ar atoms in solid argon is -3.8 A. The polarizability of argon is 1.66 x 1030 m3, and the first ionization energy is 1521 kJ mor' a. Estimate the boiling point of argon. [Hint: Calculate the potential energy due to dispersion interaction for solid argon, and equate this quantity to the average kinetic energy of 1 mole of argon gas, which is (3/2) RT] b. The actual boiling point of argon is 88 K. Explain any difference between the calculated and actual values.

Explanation / Answer

a) we know that

at boiling point

potential energy = kinetic energy

aslo

average kinetic energy of a gas = 1.5 RT

so

1.4 x 1000 = 1.5 x 8.314 x T

T = 112

so

the boiling point of argon is 112 K

b)

given

that

actual boiling point of argon is 88 K

estimated boiling point is 112 K

so

there is a difference between both the values

this difference is due to the dispersions forces for interaction between the atoms

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