4) The van der Waals constants a and b (molar versions rather than my idiosyncra

Question

4) The van der Waals constants a and b (molar versions rather than my idiosyncratic per particle versions) for water are: a = 0.5801 m^3 mol^-2 and b = 3.19.10^-5 m^-3 mol^-1 . Assuming that water is a Van der Waals fluid find the critical point temperature. critical point pressure and the critical point density predicted by the Vander Waals equation for water. Compare your results with the actual values of the critical point parameters which are: Tc = 647.3 K, Pc - 22.12 MPa, and Pc = 348 kg/m^3. What is the percent error of the van der Waals prediction of water's critical temperature, pressure, and density? BTW, the molar mass of water is 0.0180152 kg/mol.

Explanation / Answer

given

a=0.58 J/m^3.mol^-2

b=3.19*10^-5 m^3/mol

critical point temparature Tc=8a/27Rb

=8*0.58/27*8.314*3.19*10^-5

=647.9679 K

============

Pc=a/27b^2

=0.58/27*(3.19*10^-5)^2

=21.1097*10^6 Pa

=21.1097 Mpa

===========

and

Vc=3b

=3*3.19*10^-5

=9.57*10^-5 m^3 .............................

now

n=PV/RT

=(21.1097*10^6*9.57*10^-5)/(8.314*647.9679)

=0.377 mol ..................................

m=n*M

=0.375*0.0180152

=0.006755 kg

critical density rho=0.006755/9.57*10^-5

=70.585 kg/m^3 ...............................

error of temparature(in %)=(647.9679-647.3)/647.3

=0.103%

error of pressure(in %)=(22.12*10^6-21.1097*10^6)/22.12*10^6

=4.56%

error of density(in %)=(348-70.585)/348

=79.71 %

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