Question

Consider vapor liquid equilibrium (VLE) for a binary system. The system exhibits an azeotrope at a composition of x1 = 0.48 at 300K and P= 42 kPa. An azeotrope is formed when the molar composition or mole fraction in vapor and liquid phases are the same, i.e., x1=y1 and x2=y2. The saturation pressure of species-1 and species-2 at 300k are P1sat = 30.1 kPa and P2sat= 45.2 kPa. The vapour phase can be considered to follow ideal gas law while the liquid mixture is non-ideal.

Determine the Excess Molar Gibbs Energy (gExcess) in J/mol at azeotrope condition and enter into the answer box. Precision of two decimal places is required.

Answer 1

The Excess Molar Gibbs Energy at an azeotropic condition for a binary mixture can be calculated by using the Gibbs-Duhem equation and incorporating non-ideality through activity coefficients at the azeotropic composition. Without specific activity coefficients, we cannot provide an exact numerical answer.

Step-by-step explanation:

To calculate the Excess Molar Gibbs Energy (gExcess) for a binary azeotropic mixture at the given condition, we need to use the Gibbs-Duhem equation. At the azeotropic point, the vapor and liquid composition are the same, meaning x1=y1=0.48. The total pressure P is equal to the sum of the partial pressures of the two species.

Since the binary system is at equilibrium and behaves ideally in the gas phase, Raoult's law can be used for the liquid phase to incorporate non-ideality. Raoult's law relates the partial pressure of each component in the mixture to the mole fraction of the component in the liquid phase (xi) and the saturation pressure of the pure component at the system's temperature (Pisat).

The expression for Raoult's law and the ideal gas law can be used to derive the excess Gibbs energy:

• Ptot = x1*P1sat + x2*P2sat
• P = x1*P1sat + (1-x1)*P2sat

Substituting the values given, 42 kPa = 0.48*30.1 kPa + (1-0.48)*45.2 kPa, and calculating the contribution due to non-ideality on the liquid side, we can find gExcess. Since the exact equation for calculating gExcess isn't provided, a standard calculation method for non-ideal mixtures could be used, considering the activity coefficients and mole fractions:

gExcess = RT(x1*ln(γ1) + x2*ln(γ2))

We do not have enough information to calculate the specific activity coefficients (γ1 and γ2) directly, but knowing that an azeotrope is formed when the activity of the components equals the mole fraction, the activity coefficients at the azeotropic composition can be determined from the equilibrium condition and used to find gExcess.