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When the oxide of generic metal M is heated at 25.0 ∘C , a negligible amount of M is produced.
MO2(s) ⇌ M(s) + O2(g) ΔG∘=290.5 kJmol
When this reaction is coupled to the conversion of graphite to carbon dioxide, it becomes spontaneous.
What is the chemical equation of this coupled process? Show that the reaction is in equilibrium. Include physical states and represent graphite as C(s) .
The Gibbs free energy variation for spontaneous reactions is always less than zero . This can be measured using the Gibbs-free energy the formation of the species within the reactions. ......... ADVERTISEMENT ......... ..8..♦ Relevant knowledgeSpontaneous Reaction
We are given the following reaction:
MO2(s) ⇌ M(s) + O2(g) ΔG = 290.5 kJ/mol
The reaction mentioned above is connected with the transformation of graphite into carbon dioxide. The reaction then turns spontaneous.
C(s) + O2(g)→ CO2(g) ΔG = −394.5 kJ/mol
Chemical reaction:
MO2(s) + C(s)→M(s) + CO2(g)
ΔG = 290.5 kJ/mol − 394.5 kJ/mol = −104.0 kJ/mol
The Gibbs free energy shift of the reaction is negative once the oxide of the generic metal (M) is joined with graphite. Thus, the reaction is spontaneous.
The equilibrium constant of the coupled reaction may be calculated by:
ΔG = −RTln(K)
ln(K) = ΔG/RT
ln(K) = (−104.0 kJ/mol) / (−8.314 J/K⋅mol × 298 K)
ln(K) = 42.0
K = 1.77×1018