Calculate the change in molar Gibbs energy of carbon dioxide (treated as a perfect gas) at 20°C

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, (b) 0.00027 atm, its partial pressure in air.

Solutions

Expert Solution

Solution : Calculate the change in molar Gibbs energy of carbon dioxide

a. From 1.0 bar to 2.0 bar

By the formula ΔG_m = RT ln(P_f/P_i) (perfect gas).

Parameter	Value
R	8.314 J/molK
T	293 K
P_f	2.0 bar = 2 x 10⁵ Pa
P_i	1.0 bar = 1 x 10⁵ Pa

Then ΔG_m = 8.314 x 293 x ln(2 x 10⁵/1 x 10⁵) = 1680.84 J/mol

Therefore, The change in molar Gibbs energy is	ΔG_m = 1680.84 J/mol

b. From 1 bar to 0.00027 atm

From the formula ΔG_m = RT ln(P_f/P_i) (perfect gas).

Parameter	Value
R	8.314 J/molK
T	293 K
P_f	0.00027 atm = 25 Pa
P_i	1.0 bar = 10⁵ Pa

Then ΔG_m = 8.314 x 293 x ln(25/10⁵) = -4165.56 J/mol

Therefore, The change in molar Gibbs energy is	ΔG_m = -4165.56 J/mol

a. Therefore, ΔG_m = 1680.84 J/mol

b. Therefore, ΔG_m = -4165.56 J/mol

SUN BUNRA answered 6 months ago

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