— Physical Chemistry — Thermodynamics Chemistry Question
Expansion of Ideal Gas and Thermodynamics of Liquid Mixing
A quantity of 0.10 mol of an ideal gas A initially at 22.2 o C is expanded from 0.200 dm 3 to 2.42 dm 3 . Calculate the values of work (w), heat (q), internal energy change (U), entropy change of the system (Ssys), entropy change of the surroundings (Ssurr), and total entropy change (Suniv) if the process is carried out isothermally and irreversibly against an external pressure of 1.00 atm.
Model Answer
U = 0, q = -w
w = – (1.00 atm) × (2.42 – 0.200 dm 3 ) × (101.325 J dm -3 atm -1 )
= – 225 J
q = 225 J
Ssurr = – 225 J/295.4 K = – 0.762 J K -1
Ssys = 0.100 mol × 8.3145 J mol -1 K -1 × 295.4 K × / (295.4 K)
= 2.07 J K -1
Suniv = 2.07 + (– 0.762) = 1.31 J K -1
If 3.00 mol of A is condensed into liquid state and is mixed with 5.00 mol of liquid B, calculate the changes in entropy and Gibbs free energy upon such mixing at 25.0 C. This mixture can be assumed to be ideal.
Model Answer
H mix = V mix = 0
The other functions are given by these equations:
The mole fraction of A is 3.00 / (3.00 + 5.00) = 0.375.
The mole fraction of B is 1.000 – 0.375 = 0.625.
ΔG mix = 8.314 J mol -1 K -1 × 298.0 K × (0.375×ln 0.375 + 0.625×ln 0.625) =
= – 1639 J mol -1
ΔS mix = – 8.314 J mol -1 K -1 × (0.375×ln0.375 + 0.625×ln0.625) = 5.50 J K -1 mol -1