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?

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