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Answer :
Final answer:
The standard Gibbs free energy change (ΔG°) at 900 K for the decomposition of hydrogen sulfide is calculated using the Gibbs-Helmholtz equation, yielding a value of e) 99.1 kJ.
Explanation:
To find the standard Gibbs free energy change (ΔG°) at 900 K for the decomposition of hydrogen sulfide, we use the Gibbs-Helmholtz equation:
ΔG° = ΔH° - TΔS°
Where ΔH° is the standard enthalpy change, ΔS° is the standard entropy change, and T is the temperature in Kelvin.
Firstly, we convert ΔH° from kilojoules to joules:
169.4 kJ = 169400 J
Then, we plug in the values into the equation at 900 K:
ΔG°(900 K) = 169400 J - (900 K × 78.1 J/K)
ΔG°(900 K) = 169400 J - 70300 J
ΔG°(900 K) = 99000 J or 99 kJ
Thus, the value of ΔG° at 900 K is 99.1 kJ (Option e).
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Rewritten by : Barada
The correct option is e. 99.1 kJ.
The correct calculation is as follows:
[tex]\[ \Delta G^\circ(900 \, \text{K}) = 146.1 \, \text{kJ} + (602 \, \text{K}) \times 0.0781 \, \text{kJ/K} - 900 \, \text{K} \times \ln\left(3.0199\right) \times 0.0781 \, \text{kJ/K} \] \[ \Delta G^\circ(900 \, \text{K}) = 146.1 \, \text{kJ} + 47.1742 \, \text{kJ} - 900 \, \text{K} \times 1.0986 \times 0.0781 \, \text{kJ/K} \][/tex]
[tex]\[ \Delta G^\circ(900 \, \text{K}) = 146.1 \, \text{kJ} + 47.1742 \, \text{kJ} - 81.4295 \, \text{kJ} \] \[ \Delta G^\circ(900 \, \text{K}) = 193.2742 \, \text{kJ} - 81.4295 \, \text{kJ} \] \[ \Delta G^\circ(900 \, \text{K}) = 111.8447 \, \text{kJ}\][/tex]
