Lattice Models for Fluids - Regular Solution Model

[mille2eo]

1.
Problem Statement:

For the regular solution model, develop the equations for the compositions of the coexisting phases in a binary system and plot the phase boundary as a function of χ/RT.2. This question stems from Sandler's Introduction to Applied Statistical Thermodynamics.

The Attempt at a Solution

I am having trouble understanding how to approach this problem. I know that the equations I need to develop are a function of x1, x2 -> (1-x1). I do not know where to start when considering an equation for a phase boundary.

Any help would be appreciated. [/B]

 

[Asim Riaz]

The solution to this problem can be found by using the Gibbs phase rule. According to the Gibbs phase rule, the number of degrees of freedom in a two-component system is equal to the number of components minus one. In a two-component system, the equation for the compositions of the coexisting phases is: x1 + x2 = 1 where x1 and x2 are the mole fraction of each component. To plot the phase boundary as a function of χ/RT, we need to solve for the mole fraction of each component at different values of χ/RT. This can be done by rearranging the equation above to solve for either x1 or x2, depending on which component we want to solve for. For example, if we want to solve for x1, we can rearrange the equation to give us: x1 = 1 - x2 This equation can then be used to plot the phase boundary as a function of χ/RT.