Question

# ± Gibbs Free Energy: Temperature Dependence Gibbs free energy (G) is a measure of the spontaneity...

± Gibbs Free Energy: Temperature Dependence Gibbs free energy (G) is a measure of the spontaneity of a chemical reaction. It is the chemical potential for a reaction, and is minimized at equilibrium. It is defined as G=H−TS where H is enthalpy, T is temperature, and S is entropy.

The chemical reaction that causes aluminum to corrode in air is given by

4Al+3O2→2Al2O3

in which at 298 K

 ΔH∘rxn = −3352 kJ ΔS∘rxn = −625.1 J/K

Part A

What is the standard Gibbs free energy for this reaction? Assume the commonly used standard reference temperature of 298 K.

Part B

What is the Gibbs free energy for this reaction at 5975 K ? Assume that ΔH and ΔS do not change with temperature.

Express your answer to two decimal places and include the appropriate units.

Part C

At what temperature Teq do the forward and reverse corrosion reactions occur in equilibrium?

A)

we know that

dGo = dHo - TdSo

so

dGo = (-3352 x 1000) - ( 298 x -625.1)

dGo = -3165.72

so

standard gibbs free energy is -3165.72 kJ

B)

now

dG = dH - TdS

given

dH and dS do not change

and

T = 5975 K

so

dG = ( -3352 x 1000) - ( 5975 x -625.1)

dG = 382.9725 kJ

so

at 5975 K

gibbs free energy for this reactioon is 382.9725 kJ

C)

we know that

at equilibrium

dG= 0

so

dH - TdS= 0

dH = TdS

T = dH / dS

so

T = -3352 x 1000 / -625.1

T = 5362.34

so

at 5362.34 K , it will be at equilibrium

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