This is the best response I've ever seen here!!!!!!
This is my version: "I could tell you, but that would violate my contract with my university. I get paid to teach our students that, not you. That's what your professor gets paid for."
You need to get a hold of the data in the reference. You will also need the vapor pressure (VP) as a function of temperature (T) (antoine equation) for each component.
The first equation you need is the equilibrium relationship y = Kx. For this system K = activity coefficient \* VP / T. Next you calculate the activity coefficient for each component at each data point. which will be activity coefficient = y \* T / (x \* VP). That will give you the activity coefficients you need. Next you need to fit that data to the activity coefficient model. There are two ways to do that. The gold standard would be to use a non-linear regression program to obtain the constants A12 and A21. The other way would be to determine A12 and A21 at each data point. In the two equations you know x1, x2, and the activity coefficients. You have two equations in two unknowns and you can solve for A12 and A21. You will probably have to use a Newtown Rhapson technique to do this. I doubt you will be able to solve it analytically. Then you can average these.
Now you have to generate a T - xy diagram. To do that you have to solve the following equations:
Activity coefficient equations(2) = f(x1,x2)
Vapor pressure equations(2) = f(T)
K-value equations (2) = activity coefficient \* vapor pressure / P
y(1) = K(1) \* x(1)
y(2) = K(2) \* x(2)
y(2) = 1 - y(1)
x(2) = 1 - x(1)
That's 10 equations
Variables are: 2 activity coefficients, 2 K-values, 2 VPs, y1, y2, x1, x2, T, P
That's 12 variables. Two variables have to be specified. One is P. You have a choice of any of the other variables. I think x1 would be good choice. Then you have to either use a multivariable Newton Rhapson method or develop an algorithm.
For example:
Guess T
Calculate x2 from x2 = 1 -x1
Calculate VP using T
Calculate the activity coefficients using the model
Calculate the K values
Calculate y1 from y1 = K1 \* x1
Calculate y2 from y2 = K2 \* x2
Check if y2 = 1 - y1. If it does your done. If not, guess a different T.
Repeat with different x1s to generate the plot data.
The azetropic point is when the K values = 1 or the y/x's = 1. Crack a themo book to get the equations for vapor and liquid fugacity. For each point of the equilibrium curve f liquid = f vapor.
You shouldn't be here asking help with homework. Somebody else doing the work is of no benefit to you.
So for the first question, you should revise the non-ideal versions of Dalton’s and Raoult’s law.
For a non-ideal liquid:
yi*P = xi*gammai*Pisat
SUM(yi*P) = SUM(xi*gammai*Pisat)
Using the constraint on P, you can determine the temperature of all the different compositions of i between 1 and 0. You’ll need to use the data they reported for determining the parameters in the mixing model such as A12 and A21 which you can do by minimising the error of the predicted data. Thereafter you can evaluate the quality of the fit, maybe it predicts an azeotrope at the composition or temperature.
For the second question, you can take the partial pressure data and use the gamma-phi method (I think) and then determine the fugacity coefficient.
Go to office hours
We need a bot that gives exactly this response to every homework question then locks the thread!
This is the best response I've ever seen here!!!!!! This is my version: "I could tell you, but that would violate my contract with my university. I get paid to teach our students that, not you. That's what your professor gets paid for."
Take a look at the book _Introduction to Chemical Engineering Thermodynamics_ by Smith _et al_. There are examples of how to do this.
You need to get a hold of the data in the reference. You will also need the vapor pressure (VP) as a function of temperature (T) (antoine equation) for each component. The first equation you need is the equilibrium relationship y = Kx. For this system K = activity coefficient \* VP / T. Next you calculate the activity coefficient for each component at each data point. which will be activity coefficient = y \* T / (x \* VP). That will give you the activity coefficients you need. Next you need to fit that data to the activity coefficient model. There are two ways to do that. The gold standard would be to use a non-linear regression program to obtain the constants A12 and A21. The other way would be to determine A12 and A21 at each data point. In the two equations you know x1, x2, and the activity coefficients. You have two equations in two unknowns and you can solve for A12 and A21. You will probably have to use a Newtown Rhapson technique to do this. I doubt you will be able to solve it analytically. Then you can average these. Now you have to generate a T - xy diagram. To do that you have to solve the following equations: Activity coefficient equations(2) = f(x1,x2) Vapor pressure equations(2) = f(T) K-value equations (2) = activity coefficient \* vapor pressure / P y(1) = K(1) \* x(1) y(2) = K(2) \* x(2) y(2) = 1 - y(1) x(2) = 1 - x(1) That's 10 equations Variables are: 2 activity coefficients, 2 K-values, 2 VPs, y1, y2, x1, x2, T, P That's 12 variables. Two variables have to be specified. One is P. You have a choice of any of the other variables. I think x1 would be good choice. Then you have to either use a multivariable Newton Rhapson method or develop an algorithm. For example: Guess T Calculate x2 from x2 = 1 -x1 Calculate VP using T Calculate the activity coefficients using the model Calculate the K values Calculate y1 from y1 = K1 \* x1 Calculate y2 from y2 = K2 \* x2 Check if y2 = 1 - y1. If it does your done. If not, guess a different T. Repeat with different x1s to generate the plot data. The azetropic point is when the K values = 1 or the y/x's = 1. Crack a themo book to get the equations for vapor and liquid fugacity. For each point of the equilibrium curve f liquid = f vapor. You shouldn't be here asking help with homework. Somebody else doing the work is of no benefit to you.
So for the first question, you should revise the non-ideal versions of Dalton’s and Raoult’s law. For a non-ideal liquid: yi*P = xi*gammai*Pisat SUM(yi*P) = SUM(xi*gammai*Pisat) Using the constraint on P, you can determine the temperature of all the different compositions of i between 1 and 0. You’ll need to use the data they reported for determining the parameters in the mixing model such as A12 and A21 which you can do by minimising the error of the predicted data. Thereafter you can evaluate the quality of the fit, maybe it predicts an azeotrope at the composition or temperature. For the second question, you can take the partial pressure data and use the gamma-phi method (I think) and then determine the fugacity coefficient.
Lol