The molar free energy (J mol^-1) of a liquid solution of a binary A-B alloy as a function of temperature ( T ) and composition (x, the mole fraction of B) is given by:

𝐺^𝐿(𝑇, 𝑥) = (1 − 𝑥)𝐺^0,𝐿 + 𝑥𝐺^0,𝐿 + 𝑅𝑇[𝑥 ln 𝑥 + (1 − 𝑥) ln(1 − 𝑥)] + 4000𝑥(1 − 𝑥).

where 𝐺^0,𝐿 and 𝐺^0,𝐿 are the molar free energies of pure liquid A and pure liquid B. What is the excess molar free energy, 𝐺^{𝑋𝑆,𝐿}, for an alloy with 𝑥 = 0.5 at 𝑇 = 1000 K? Given: Gas constant R = 8.314 J K^-1 mol^-1

(A) 1000 J mol^-1        (B) – 2000 J mol^-1     

(C)  4763 J mol^-1                           (D) – 5763 J mol^-1