1. The total moles of the solution is 0.3079193 mol.
2. The mole fraction for gold is 0.2473212, and for silver, it is 0.7526787.
3. The molar entropy of mixing for gold is 2.87285 j/K, while for silver, it is 1.77804 j/K.
4. The total entropy of mixing sums to 4.65089 j/K.
5. Molar free energy amounts to -2325.445 kJ.
6. Chemical potential for silver is -1750.31129 j/mol and for gold, it is -575.13185 j/mol. To elaborate:
(1) The molar mass of silver stands at 107.8682 g/mol, and gold's at 196.96657 g/mol. Hence, calculating moles leads to mass/molar mass for silver: 25 g/107.8682 g/mol = 0.2317643 mol and for gold: 15 g/196.96657 g/mol = 0.076155 mol, resulting in a total of 0.30791193 mol.
(2) For the mole fractions, silver's fraction is 0.2317643/0.3079193 = 0.7526787, and for gold, it's 0.076155/0.3079193 = 0.2473212.
(3) To find molar entropy mixing ∆Sm, we use the formula ∆Sm = -R * Xi * ln(Xi) where R = 8.3144598. For silver, substituting gives us 1.77804 j/K, while for gold, we get 2.87285 j/K.
(4) Overall entropy of mixing totals 4.65089 j/K thus calculated.
(5) The Gibbs free energy at 500 °C can be derived through G = H - TS, accounting to H = 0 (as T is 500 + 273 = 773 K and S is 4.65089), resulting in G equating to -3595.138 kJ.
(6) The chemical potentials calculated derive from multiplying the Gibbs free energy by their mole fractions.
Calculation yields 209.53. The molar concentration is calculated by moles divided by volume. Given the volume of 750 mL, which translates to 0.75 L, the moles of CuBr₂ can be determined as molar concentration multiplied by volume, resulting in 1.25 × 0.75 = 0.9375. Mole count is derived from the mass of CuBr₂ divided by its molecular mass. The molecular mass of CuBr₂ is computed as 63.5 + 80 × 2 = 223.5, where the mass of Cu is 63.5 and that of Br is 80. Consequently, the mass needed amounts to 223.5 × 0.9375 = 209.53 g.
