It can be shown by statistical thermodynamics that the entropy of monatomic flui

Question

It can be shown by statistical thermodynamics that the entropy of monatomic fluids is S = Nk_B{5/2 + ln[(2 pi mk_B T)^3/2/h^3 V/N]}, where N is the number of molecules and V is the volume (a) Estimate the molar entropies of Argon liquid and vapor at its normal boiling point (T_nb = -185.8 degree C). For your information, liquid Ar has a density of 1.3954 g/cm^3. (b) Estimate the numbers of microstates generated by one mole of Ar vapor at its T_nb. (c) The Sackur-Tetrode equation estimates delta S^vap almostequalto S^vap = Nk_B{5/2 + ln[(2 pi mk_BT)^3/2/h^3 V/N]}. Use your result from (a) to verify if it is reasonable. (d) Considering delta H^vap = T delta S^vap, use the Sackur-Tetrode equation to estimate delta H^vap for Ar at its T_nb and determine the %error based on the experimental value of 6.53 kJ/mol.

Explanation / Answer

The number of microstates of argon at its normal boilng point can be calculated by using the relation:

S = kB lnW

where kB = Boltzmann’s constant = 1.381 × 1023 J/K

W = number of microstates

As the number of microstates, W, increases, the entropy, S, increases logarithmically. Boltzmann’s constant, kB, is a proportionality constant in this equation and has the same units as entropy, energy/kelvin (J/K).

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