Question

When the oxide of generic metal m is heated at 25.0 °c, only a negligible amount of m is produced. o2m(s ----> m(s o2(g delta g= 288.9 kj/mol 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. i got an answer of : o2m(s c(s ----> m(s co2(g this is correct. i need help on this part of the question: what is the thermodynamic equilbrium constant for the coupled reaction? i attempted this twice and got k=1.22 and 0.89 and they are both wrong. please help?

Answer 1

(1) MO₂(s) + C(s) → M(s) + CO₂ (g),  ΔG₁ = 288.9 kJ/mol
(2) C(s) + O₂(g) → CO₂(g),   ΔG₂ = -394.4 kJ/mol
By adding both equations 1 + 2 we get the coupled reaction:
MO₂(s) + 2 C(s) + O₂(g) → M(s) + 2 CO₂(g)
ΔG⁰ = ΔG₁ + ΔG₂ 
       = 288.9 + (-394.4) = -105.5 kJ/mol = -105500 J/mol
Temperature T = 25 + 273.15 = 298.15 K
Molar gas constant R = 8.314 J/mol.K
K = $e^{ \frac{-dG0}{RT} }$
   = $e^{ \frac{105500}{8.314 x 298.15} }$ 
    = 3.05 x 10¹⁸