# How to express van der waals equation as virial expansion?

1. Feb 7, 2009

### Chaste

1. The problem statement, all variables and given/known data

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.
(Hint. The expansion you will need is (1–x) -1 = 1+x+x2+... . Series expansions
are discussed in Appendix 2 of Atkins.)
Measurements on argon gave B=-21.7 cm3.mol-1 and C=1,200 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?

2. Relevant equations
Van der waals equation of state : ( p + a / V^2 ) ( V-b ) = RT

3. The attempt at a solution
Apparently this question is very common and found throughout the web. But I couldn't find any solution. I don't even know how to begin with expressing ;(
please help. thanks.

2. Feb 7, 2009

### chrisk

Solve for P giving you a term containing

$$\frac{1}{V_m-b}$$

Factor out Vm then use the hint.

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