Final answer:
The second virial coefficient of O2 is calculated as the negative value of the van der Waals constant b. The third virial coefficient is approximate and related to both van der Waals constants a and b. Exact calculations would require further refinement.
Step-by-step explanation:
To calculate the second and third virial coefficients (B and C) of O2 from its van der Waals constants, we need to use the relations derived from the van der Waals equation and compare to the generalized virial equation of state. The van der Waals equation is an improvement on the ideal gas law and takes into account the finite size of molecules and the intermolecular attractions.
The van der Waals equation is written as:
(P + a/V2) (V - b) = RT
Where P is the pressure, V is the molar volume, T is the absolute temperature, R is the universal gas constant, and a and b are the van der Waals constants specific to the gas.
For the second virial coefficient B, we can equate:
B = -b
Using the given value for b (3.18 × 10-5 m3/mol), we get:
B = -3.18 × 10-5 m3/mol
To obtain the third virial coefficient C, it's necessary to expand the van der Waals equation and match terms with the virial expansion of the pressure in powers of density. This calculation is more complex and beyond the scope of a general explanation but involves the constant a, hence:
C ≈ a - b2
Using the given value for a (0.138 J·m3/mol2), after proper unit conversion if needed, we can compute an approximate value for C. However, please note that this approximation might not be sufficiently accurate for all applications, and alternative methods may be required for precise calculations.