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Answer :
The standard Gibbs free energy change (∆G°) for the reaction 2 NOâ‚‚(g) → Nâ‚‚Oâ‚„(g) at 25 °C is 93.0 kJ/mol. The spontaneity of a reaction is determined by the Gibbs free energy change (∆G).
A reaction is spontaneous if ∆G is negative (∆G < 0), indicating that the reaction can proceed without the input of external energy.
The equation for calculating ∆G is:
∆G = ∆H - T∆S
Where:
∆H = enthalpy change
T = temperature in Kelvin
∆S = entropy change
Given:
∆H = 25.00 kJ/mol
∆S = 238.0 J/mol K
Temperature (T) = 25.00 °C = 298.15 K (convert to Kelvin)
Let's calculate ∆G:
∆G = (∆H * 1000) - (T * ∆S)
∆G = (25.00 kJ/mol * 1000) - (298.15 K * 238.0 J/mol K)
∆G = 25,000 J/mol - 71,043.7 J/mol
∆G = -46,043.7 J/mol
Since the value of ∆G is negative (-46,043.7 J/mol), the reaction is spontaneous at 25.00 °C.
To determine ∆G° for the reaction 2 NOâ‚‚(g) → Nâ‚‚Oâ‚„(g), we can use the standard Gibbs free energy of formation values (∆G°f) for the substances involved.
∆G° = ∑∆G°f (products) - ∑∆G°f (reactants)
Given:
∆G°f(NOâ‚‚) = 51.3 kJ/mol
∆G°f(Nâ‚‚Oâ‚„) = 97.8 kJ/mol
∆G° = (2 * ∆G°f(Nâ‚‚Oâ‚„)) - (2 * ∆G°f(NOâ‚‚))
∆G° = (2 * 97.8 kJ/mol) - (2 * 51.3 kJ/mol)
∆G° = 195.6 kJ/mol - 102.6 kJ/mol
∆G° = 93.0 kJ/mol
Therefore, the standard Gibbs free energy change (∆G°) for the reaction 2 NOâ‚‚(g) → Nâ‚‚Oâ‚„(g) at 25 °C is 93.0 kJ/mol.
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