Calculate the change in molar Gibbs energy of carbon dioxide (treated as a perfect gas) at 20°C when its pressure is changed isothermally from 1.0 bar to (a) 2.0 bar and (b) 0.000 27 atm, its partial pressure in air.

a) ΔG = 1688.5 J/mol = 1.7  kJ/mol

b) ΔG = 21673.3  J/mol = 21.7  kJ/mol

Explanation:

Step 1: Data given

Temperature = 20.0 °C = 293 K

Initial temperature = 1.0 bar = 0.986923 atm

Final temperature = 2.0 bar = 1.97385 atm

Step 2: Calculate

ΔG = RT * ln (Pt / Pi)

⇒with R = 8.314 J/K* mol

⇒with T = 293K

⇒with Pt = final pressure = 1.97385 atm

⇒with Pi = the initial pressure = 0.986923 atm

ΔG = 8.314 J/mol*K *293 K * ln (1.97385/0.986923)

ΔG = 8.314 J/mol*K *293 K * 0.693

ΔG = 1688.5 J/mol = 1.7  kJ/mol

(b) 0.000 27 atm

Step 3:

ΔG = RT * ln (Pt / Pi)

⇒with R = 8.314 J/K* mol

⇒with T = 293K

⇒with Pt = final pressure = 1.97385 atm

⇒with Pi = the initial pressure = 0.00027 atm

ΔG = 8.314 J/mol*K *293 K * ln (1.97385/0.00027)

ΔG = 8.314 J/mol*K *293 K * 8.897

ΔG = 21673.3  J/mol = 21.7  kJ/mol

it is the most commonly accepted one