Answer:
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
