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28 September, 14:09

15 g of gold and 25 g of silver are mixed to form a single-phase ideal solid solution.

How many moles of solution are there? What are the mole fractions of gold and silver?

What is the molar entropy of mixing?

What is the total entropy of mixing?

What is the molar free energy change at 500 degree C?

What are the chemical potentials of Au and Ag at 500 degree C taking the free energies of pure Au and Ag as zero?

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  1. 28 September, 14:59
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    1. How many moles of solution are there. Ans: 0.3079193mol

    2. Mole fraction for gold : 0.2473212

    Mole fraction for silver: 0.7526787

    3. Molar entropy of mixing for gold: 2.87285j/k

    Molar entropy of mixing for silver: 1.77804j/k

    4. Total entropy of mixing: 4.65089j/k

    5. Molar free energy: - 2325.445kj

    6. Chemical potential for silver: - 1750.31129j/mol

    Chemical potential for gold: - 575.13185j/mol

    Explanation:

    (1)

    molar mass of silver = 107.8682g/mol

    Molar mass of gold = 196.96657g/mol

    Therefore mole = mass/molar mass

    For silver: 25g/107.8682g/mol = 0.2317643mol

    For gold: 15g/196.96657g/mol = 0.076155mol

    Total number of mole = 0.2317643+0.076155 = 0.30791193mol

    (2)

    Mole fraction for silver = 0.2317643/0.3079193 = 0.7526787

    Mole fraction for gold=0.076155/0.3079193=0.2473212

    (3)

    The molar entropy mixing ∆Sm = - RXi*lnXi

    R = gas constant = 8.3144598

    Xi = mole fraction

    For silver:

    -8.3144598*0.7526787 (ln0.7526787) = 1.77804j/k

    For gold:

    -8.3144598*0.2473212 (ln0.2473212) = 2.87285k/j

    (4)

    Total entropy = 1.77804+2.87285=4.65089k/j

    (5)

    Molar free energy change at 500°C

    G=H-TS

    Where G = Gibbs free energy

    H = enthalpy,. T = Temperature, S = entropy

    H=0, T=500 + 273=773k, S=4.65089

    Therefore

    G = 0 - 773x4.65089 = - 3595.138kj

    (6)

    Chemical potential = Gibbs free energy * mole fraction

    For silver:

    -3595.138*0.7526787=-2705.9837j/mol

    For gold:

    -3595.138*0.2473212 = - 889.15381j/mol
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