With reference to Ex. 10.4 (a) Apply Eq. (10.7) to Eq. (A) to verify Eqs. (B) and

Question:

With reference to Ex. 10.4
(a) Apply Eq. (10.7) to Eq. (A) to verify Eqs. (B) and (C).
(b) Show that Eqs. (B) and (C) combine in accord with Eq. (10.11) to regenerate Eq. (A).

Eq. (10.11)

(c) Show that Eqs. (B) and (C) satisfy Eq. (10.14), the Gibbs/Duhem equation.
(d) Show that at constant T and P,
(dH̅₁/ dx₁) _x1=1 = (dH̅₂/ dx₁) x₁₌₀ = 0
(e) Plot values of H, H̅₁ , and H̅₂ , calculated by Eqs. (A), (B), and (C), vs. x₁. Label points H₁, H₂, H̅^∞₁ , and H̅^∞₂ , and show their values.

Ex. 10.4

The enthalpy of a binary liquid system of species 1 and 2 at fixed T and P is represented by the equation:

H = 400_x1 + 600_x2 + x₁ x₂ (40x₁ + 20x₂)

where H is in J·mol^–1. Determine expressions for H̅1 and H̅2 as functions of x₁, numerical values for the pure-species enthalpies H₁ and H₂, and numerical values for the partial enthalpies at infinite dilution H̅∞₁ and H̅^∞₂.

Eq. (10.7)

(A) & (B) Eq. (10.7) & (10.11) (A) (B) (C)

Eq. (10.7). For binary systems, however, an alternative procedure may be more convenient. Written for a binary solution, the summability relation, Eq. (10.11), becomes: