In a binary flash calculation show the following are satisfi

In a binary flash calculation, show the following are satisfied:

x1=(1-K2)/(K1-K2)

y1=[K1(1-K2)]/(K1-K2)

and

V=[z1(K1-K2)-(1-K2)]/[(K1-1)(1-K2)]

Solution

The simplest procedure is to consider benzene and toulene and choose a temperature T between 377.31 K and 409.33 K, evaluate the vapor pressures, and solve for x and y from the following equations:

y_i/x_i = P_i^sat/ P

Therefore,

y₁ = K₁*x₁ (Equation 1)

Also,

y₂ = 1-y₁

x₂ = 1-x₁

Hence,

1-y₁/1-x₁ = K₂

1-y₁ = K₂*(1-x₁ ) (Equation 2)

Substituting equation 2 into equation 1 yields :

1- K₁*x₁ = K₂*(1-x₁ )

x₁ = (1 - K₂ ) / ( K₁ - K₂ )

y₁ = K₁*x₁