Question

AN IDEAL SOLUTION IS MADE FROM 6.00 MOLES OF BENZENE & 2.50 MOLES OF TOLUENE CALCULATE ΔG MIXING AT 298 K & 1 BAR PRESSURE

Answer 1

Formula of Gibbs free energy of mixture is given by
$\bold{\Delta_\text{mix}G= nRT(x_1\ln x_1 +x_2\ln x_2)}$
Where x₁ is the mole fraction of benzene ,
x₂ is the mole fraction of toluene ,
n is the total number of moles
R is the universal gas constant e.g., R = 25/3 J/Kmol
T is the temperature .

Now, x₁ = (n₁)/(n₁ + n₂) = 6/(6 + 2.5) = 6/8.5 = 12/17
x₂ = n₂/(n₁ + n₂) = 2.5/(6 + 2.5) = 5/17

Now, $\bold{\Delta G_{mix}= nRT(x_1 lnx_1+x_2 lnx_2)}$
n = n₁ + n₂ = 6 + 2.5 = 8.5
R = 25/3 J/Kmol
T = 298K
∴ $\bold{\Delta G_{mix}}$ = 8.5 × 25/3 × 298 [12/17ln(12/17) + 5/17ln(5/17)]
=12.5 × 298/3 [12ln(12/17) + 5ln(5/17) ] J
= 12.5 × 298/3 × (-10.2985) = -12.787 kJ