Question

Solve the given system of equation (VanLaar activity coefficient model) for A12 and A21. Given that 2 In 71 = A12 ) A21 X2 A12X1 +A21 X2 A12X1 A12 X1 +A21 X2 2 In 72 = A21 and Y1 1.319, Y2 = 1.353, X1 = = 0.628 and X1 + x2 = 1

Answer 1

To solve for the Van Laar constants A12 and A21, we use the given activity coefficients and mole fractions to form a system of equations. These are then solved using the provided numerical values, potentially with the use of iterative methods for the non-linear expressions.

Step-by-step explanation:

The Van Laar equation is used in thermodynamics to calculate the activity coefficients of components in a binary mixture. Given the equilibrium constants (γ1 and γ2) for each component in the Van Laar activity coefficient model, along with the mole fractions (X1 and X2), we can solve for the Van Laar constants A12 and A21. Using the provided formulas for activity coefficients γ1 and γ2, we can set up the following system of equations:

• 2 In γ1 = A12 - A21 X2 (A12X1 + A21 X2)
• 2 In γ2 = A21 - A12 X1 (A12X1 + A21 X2)

To solve for A12 and A21, we use the values Y1 = 1.319, Y2 = 1.353, X1 = 0.628, and X2 = 0.372 (since X1 + X2 = 1). Then we can isolate A12 and A21 by plugging in the given values into the equations and solving for the unknowns. If needed, iterative methods such as Newton-Raphson can be employed for non-linear equations like these.