When the oxide of generic metal M is heated at 25C, only a negligible amount of

Question

When the oxide of generic metal M is heated at 25C, only a negligible amount of M is produced.
MO2(s) <---> M(s)+O2(g)
delta G = 288.5 kJ/mol

1.) When the 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)

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2.) What is the thermodynamic equilibrium constant for the coupled reaction?
K = ????

Explanation / Answer

(1) (A) MO2(s) <=> M(s) + O2(g), Delta G1 = 288.5 kJ/mol

(B) C(s) + O2(g) <=> CO2(g), Delta G2 = -394.4 kJ/mol

Add equation (A) + equation (B):

MO2(s) + C(s) + O2(g) <=> M(s) + O2(g) + CO2(g)

Cancel common terms to get coupled reaction:

MO2(s) + C(s) <=> M(s) + CO2(g)

Delta Go = Delta G1 + Delta G2

= 288.5 + (-394.4)

= -105.9 kJ/mol = -105900 J/mol

(2) Temperature T = 25 deg C = 298.15 K

Molar gas constant R = 8.314 J/mol.K

Equilibrium constant K = exp(-Delta Go/RT)

= exp(105900/(8.314 x 298.15))

= 3.58 x 10^(18)

(Note: If you use T = 298 K, then K = 3.66 x 10^18)

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