Chemical thermodynamics, entropy, Maxwell relation and Z

AI Thread Summary
The discussion revolves around calculating the molar entropy change for a gas expanding from 1 dm³ to 2 dm³ at 300 K, using the equation of state z = 1/(1-b(molar density)) with b = 0.2 dm³. The user attempts to apply the Maxwell relation and integrates to find the entropy change, initially arriving at 5.76 J, but believes they need to multiply by the compressibility factor z to reach the correct answer of 6.74 J. They express uncertainty about their method for determining molar density and the compressibility factor, trying various approaches without success. The user seeks clarification on the correct application of these thermodynamic principles in the context of a practice exam question. The discussion highlights the complexities of applying thermodynamic equations in practical scenarios.
deeko1987
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Homework Statement



A gas obeys the equation of statez=1/(1-b(molar density))

What is the molar entropy change of expanding this gas from a volume of 1 dm3 to 2 dm3 at a temperature of 300 K, given b = 0.2 dm3? Calculate your answer to three significant figures and select one answer from the list below.

You may wish to use the Maxwell relation(∂p/∂t) = ∂s/∂v LHS constant V RHS constant T

Homework Equations



PV=RT maxwell realation possibly z = PV/RT[/B]

how can I solve for the molar density to solve the compressibility factor. this is an example exam question so I already know the answer is 6.74 J

The Attempt at a Solution



I have substituted the LHS of the maxwell relationship for R/T (not sure if this is a correct assuption) then intergrated to get Rln(V2/V1)= change in entropy

this gives me 5.76 I'm assuming that this then needs multiplying by Z to get the correct answer of 6.74.

I have attempted to solve for z using the 1/volume to get molar density using both densities which give the incorrect answer. I have then tried to average the Z of both (Z1+Z2)/2 which again was a long shot, it was close but I'm assuming that is not the way its done because it seems very inaccurate to use an average for compressibility.
[/B]

Again this is not a coursework it is a multiple choice practice exam question, that gives the solution, just no feedback.
 
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