Margules' Power Series Formula: Deriving Coefficients

In summary, Margules proposed a power series formula for expressing the activity composition variation of a binary system. This formula includes coefficients αi and βi that can be determined by applying the Gibbs-Duhem equation with the assumption that coefficients higher than i=3 can be ignored. This results in a relationship between α1, β1, β2, and β3. However, the derivation of this relationship is unclear and it is unknown what the relationship would be if coefficients higher than i=4 were ignored.
  • #1
jinayb
1
0
Margules suggested a power series formula for expressing the activity composition variation of a binary system.
lnγ1=α1x2+(1/2)α2x2^2+(1/3)α3x2^3+...
lnγ2=β1x1+(1/2)β2x1^2+(1/3)β3x1^3+...
Applying the Gibbs-Duhem equation with ignoring coefficients αi's and βi's higher than i=3, we can obtain α1=β1=0, β2=α2+α3, β3=-α3

I don't know how that relationship between coefficients is derived.
Also, what would be the relationship when higher than i=4 is ignored?
Please help!
 
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  • #2
Could you elaborate a bit? E.g.

a) "Margules suggested ..." where? Reference?
b) Here is explained how you can type formulas on PF: https://www.physicsforums.com/help/latexhelp/
c) "the activity composition variation of a binary system" means what? Forces? Number system?
 
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1. What is Margules' Power Series Formula?

Margules' Power Series Formula is a mathematical equation used to calculate the coefficients of a power series. It is commonly used in thermodynamics and statistical mechanics to model the behavior of mixtures.

2. How is Margules' Power Series Formula derived?

Margules' Power Series Formula is derived using a mathematical technique called Taylor series expansion. This involves expressing a function as an infinite sum of terms, each with a different degree of the independent variable.

3. What are the applications of Margules' Power Series Formula?

Margules' Power Series Formula is commonly used in thermodynamics and statistical mechanics to model the behavior of mixtures. It can also be used in other fields such as chemistry, physics, and engineering to analyze complex systems.

4. Can Margules' Power Series Formula be used for all types of mixtures?

No, Margules' Power Series Formula is most commonly used for binary mixtures, which contain two components. It can also be extended to ternary mixtures, but it becomes more complex and less accurate for mixtures with more components.

5. Are there any limitations to using Margules' Power Series Formula?

Yes, Margules' Power Series Formula assumes ideal behavior of the components in the mixture, meaning that there are no interactions between the molecules. This may not always be the case in real-world mixtures, leading to less accurate results.

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