Express the van der waals equation of state as a virial expansion in powers of 1/vm and obtain expressions for b and c in terms of the parameters a and b. the expansion you will need is (1 − x)−1 = 1 + x + x2 + … . measurements on argon gave b = −21.7 cm3 mol−1 and c = 1200 cm6 mol−2 for the virial coefficients at 273 k. what are the values of a and b in the corresponding van der waals equation of state?

B = b -a/RT

C = b^2

a = 1.263 atm*L^2/mol^2

b = 0.03464 L/mol

Explanation:

In the given question, we need to express the van der Waals equation of state as a virial expansion in powers of 1/Vm and obtain expressions for B and C in terms of the parameters a and b. Therefore:

Using the van deer Waals equation of state:

With further simplification, we have:

Then, we have:

Therefore,

Using the expansion:

Therefore,

Thus:

          equation (1)

Using the virial equation of state:

Thus:

    equation (2)

Comparing equations (1) and (2), we have:

B = b -a/RT

C = b^2

Using the measurements on argon gave B = −21.7 cm3 mol−1 and C = 1200 cm6 mol−2 for the virial coefficients at 273 K.

" alt="cm^{3}/mol" />" /> = 0.03464 L/mol

a = (b-B)*RT = (34.64+21.7)*(1L/1000cm^3)*(0.0821)*(273) = 1.263 atm*L^2/mol^2