@ https://en.wikipedia.org/wiki/Redlich%E2%80%93Kwong_equation_of_state

I have a question regarding mixture rules of mentioned EOS & particularly the math notation that I could not comprehend

In the attached image what does this Math notation means -- annotated as 1?

e.g if I have x2 species

x1= 0.6 x2=0.4 (mol frac)
a1= 0.16 a2=0.4 (constants)

what does this notation with double summation will do with these values?

Second alternative -- annotated as 2, does it imply following construct?

1] GeomatricAVG = (0.16 * 0.14) ^ 1/2 -- 1/n where n is 2 bcz its a binary mixture
2] A = 0.6 * GeomatricAVG + 0.4 * GeomatricAVG

Wrote

In the attached image what does this Math notation means -- annotated as 1?

Hi. It means that, given the relationship between the "a's" of each component and the "a" of the mixture, you need a matrix of interaction coefficients to determine the attractive potential of molecules coefficient for the mixture, which is usually found by assuming that each coefficient in the matrix is the geometric mean of the component coefficients.

A complete example of how the Redlich-Kwong model is used for a mixture in the attached.

Redlich-Kwong.sm (23 KiB) downloaded 69 time(s).
Redlich-Kwong.pdf (93 KiB) downloaded 87 time(s).

Best regards.
Alvaro.

Joining above with this other two methods.

Redlich-Kwong - HeXe mix.pdf (136 KiB) downloaded 87 time(s).
Redlich-Kwong - HeXe mix.sm (59 KiB) downloaded 77 time(s).

Best regards.
Alvaro.

Extremely thanks for your time.

Show Spoiler

I understood. Thanks

Redlich_Kwong is an optimized version of the simpler mixture.
Optimized wrt to coefficients c1,c2 [a,b].
It might be possible to fit mixture vs some Redlich_Kwong data set.
Refactor the graphs Solver 30405.

Inst_Mixture.sm (40 KiB) downloaded 62 time(s).

I will go through Jean's file in about a day. Thanks Jean for your much needed help.