van der Waal Thermodynamics questions! The critical temperature and pressure for

Question

van der Waal Thermodynamics questions!

The critical temperature and pressure for O2 are 154.59K and 5.043 MPa, respectively. (a) Determine the constants a and b that should be used in van der Waals equation of state to ensure agreement with the critical temperature and pressure. (b) The critical molar volume of O2 is 73 cm3/mol. How well does this agree with the critical value predicted by van der Waals equation when the values of a and b determined above are used? (c) Produce a P vs. v graph containing isotherms for O2 (assuming van der Waals equation of state) at 135K, 154.59K, 250K, and 400K. On the same graph, plot isotherms at the same temperatures for the ideal gas law. Comment on the agreement/disagreement between the two sets of curves. (NOTE: van der Waals equation is not continuous at u = b . It is not necessary, nor does it really make sense, to plot your isotherms for v S b. Additionally, you may wish to display the v axis on a logarithmic scale to make the inflections in the curves at and below the critical temperature more apparent.)

Explanation / Answer

a) Tc = 8a /27XRXb

so b = 8a / 27  X R X Tc ....................1)

Pc = a/27b2..................2

Put equation 1 in 2

Pc = a / 27 X (8a / 27 R Tc)2

P c = 5.034 MPa = 5.043 X 10^6 Pascal = 49.77 atmosphere

5.043 X 10^6 = a X (8.314 X 27 X 154.59)2 / 27 X 64 X a^2

a = (8.314 X 27 X 154.59)2 / 27 X 64 X 5.043 X 10^6 =0 .138

b = 8a / 27  X R X Tc = 8 X 0.138/ 27 X 8.314 X 154.49 = 3.18 X 0^-5 m3 = 31.8 cm^3

b) The critical volume for 1 mole is Vc = 3b= 31.8X 3 = 95.4 m3

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