How to express van der waals equation as virial expansion?

In summary, the conversation is about expressing the van der Waals equation of state as a virial expansion and obtaining expressions for B and C in terms of the parameters a and b. The hint given is to use the expansion (1-x)^-1 = 1+x+x^2+... and Appendix 2 of Atkins for series expansions. The measurements on argon give values for B and C, and the goal is to find the values of a and b in the corresponding van der Waals equation of state. The solution involves solving for P and using the given hint to factor out Vm.
  • #1
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Homework Statement



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?



Homework Equations


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


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.
 
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  • #2
Solve for P giving you a term containing

[tex]\frac{1}{V_m-b}[/tex]

Factor out Vm then use the hint.
 

FAQ: How to express van der waals equation as virial expansion?

What is the Van der Waals equation?

The Van der Waals equation is a mathematical equation that describes the behavior of real gases, taking into account the intermolecular forces and the finite size of gas particles. It is an improvement over the ideal gas law, which assumes that gas particles have no volume and do not interact with each other.

How is the Van der Waals equation derived?

The Van der Waals equation is derived from the ideal gas law by incorporating two correction factors: one for the attractive forces between gas particles and one for the volume occupied by the gas particles themselves. This equation was first proposed by Johannes Diderik van der Waals in 1873.

What is the significance of expressing the Van der Waals equation as a virial expansion?

Expressing the Van der Waals equation as a virial expansion allows us to account for higher order terms in the equation, making it more accurate for describing real gases. This is especially important at high pressures where the ideal gas law breaks down.

How is the Van der Waals equation expressed as a virial expansion?

The Van der Waals equation can be expressed as a virial expansion by expanding the correction factors for attractive forces and particle volume into a series of terms. This results in a more complex equation, but it allows for more accurate predictions of gas behavior at high pressures.

What are the limitations of the Van der Waals equation?

The Van der Waals equation is still an approximation and has its limitations. It does not take into account the effects of temperature and pressure on gas behavior, and it only applies to nonpolar gases. Additionally, it may not accurately describe the behavior of gases at extreme temperatures or pressures.

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