Deriving the Wassiljewa mixture model equation

[George26]

Homework Statement

Derive the Wassiljewa mixture model equation for a binary mixture.

Relevant Equations

x1+x2 =1

Hello,

I'm in the process of deriving the Wassiljewa mixture model equation for a binary solution. I have to find an expression g^E which represents the excess g term which is added to g_IS, the ideal solution, to predict the g for a real solution. I have gotten up to a point but now I'm stuck.

I do realize that

• Setting x₁ = 1 and x₂ = 0 gives g^#(C, x₁=1) = c₁₁=g₁⁰

Any help is appreciated.

 

[Chestermiller]

It looks like you already wrote the equation for excess g at the outset. What am I missing?

 

[George26]

Hello,

I'm aiming for the form in the image attached. I'm unsure of how to get there with what I currently have.

 

[Chestermiller]

So, you are starting with

And you are trying to find the values of r and s that lead to the form of $g^E$ that you showed at the beginning of the post?

 

[Chestermiller]

What about something like this: In both expressions, let $$x_1=0.5+\delta$$and $$x_2=0.5-\delta$$Then set the two functions equal to one another at $\delta=0$ and set as many derivatives with respect to $\delta$ at $\delta=0$ as necessary to determine all the unknown constants.

 

[Chestermiller]

I think that s has to be equal to 1.