Set up a system of equations that relate the mole fractions of Q, W, Y and Z in the mixture at equilibrium to the two equilibrium constants K1 and K2. You don’t have to solve the equations, but the number of equations and unknowns must be equal such that they could be solved. Assume a reference pressure of 1 bar.

Question

The following pair of reactions is carried out in the gas phase:

Q+W ?Y

Q+Y ?Z

These compounds can be modeled using the virial equation at pressures of up to 15 bar:



And mixtures of the compounds can be modeled as an ideal solution of real gases.

A vessel initially contains 5 moles of Q and one mole of W, and the vessel is maintained at P=10 bar and T=700 K. The equilibrium constants of the reactions, K1 and K2, are both known at this temperature.

Answer 1

Equilibrium criterion for real gas:



??v_i =-1for both reactions. P and P0 are known as 10 and 1 bar respectively. K1 and K2 are considered known. The mole fractions appear to be four unknowns but can be expressed as two unknowns using the stoichiometry of the reactions:



When these four expressions are introduced into the boldfaced equilibrium equations, they become two equations in two unknowns (?1 and ?2), IF the fugacity coefficients are also evaluated. Because this is being modeled as an ideal solution of real gases, each mixture fugacity coefficient ? ? is equal to the fugacity coefficient of the pure component at the same T and P, which is ?: