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Problem 2: The molar Gibbs free energy of a binary liquid mixture at atmospheric pressure and T ? 260K is given by the following: G(x?, T) = 2.75x?? – 6.6x?3 + 0.025Tx?" – 1.16641x?" – 2x? (1) Sketch a qualitative phase diagram in the T-x? plane. (2) If the mixture shows any two-phase behavior, give the equation for the spinodal curve and calculate the spinodal composition of component 1 in two phases at 260 K. (3) Calculate any critical solution temperatures and critical composition of component 1. (4) Explain why this equation is invalid for a binary liquid mixture and violates the classical thermodynamics. Please show step-by-step derivations. (Hint: Gibbs-Duhem equation)

          Problem 2:
The molar Gibbs free energy of a binary liquid mixture at atmospheric pressure and T ? 260K
is given by the following:

G(x?, T) = 2.75x?? – 6.6x?3 + 0.025Tx?" – 1.16641x?" – 2x?

(1) Sketch a qualitative phase diagram in the T-x? plane.
(2) If the mixture shows any two-phase behavior, give the equation for the spinodal curve and
calculate the spinodal composition of component 1 in two phases at 260 K.
(3) Calculate any critical solution temperatures and critical composition of component 1.
(4) Explain why this equation is invalid for a binary liquid mixture and violates the classical
thermodynamics. Please show step-by-step derivations. (Hint: Gibbs-Duhem equation)

Problem 2:
The molar Gibbs free energy of a binary liquid mixture at atmospheric pressure and T ? 260K
is given by the following:

G(x?, T) = 2.75x?? – 6.6x?3 + 0.025Tx?" – 1.16641x?" – 2x?

(1) Sketch a qualitative phase diagram in the T-x? plane.
(2) If the mixture shows any two-phase behavior, give the equation for the spinodal curve and
calculate the spinodal composition of component 1 in two phases at 260 K.
(3) Calculate any critical solution temperatures and critical composition of component 1.
(4) Explain why this equation is invalid for a binary liquid mixture and violates the classical
thermodynamics. Please show step-by-step derivations. (Hint: Gibbs-Duhem equation)

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