# When the oxide of generic metal m is heated at 25.0 °c. only a negligible amount of m is produced.

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 = ????

(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
)

O2M(s)+ C(s) ----> M(s) + CO2(g)

I would add 288.9 to dGof for CO2 of -394.4 for -105.5 kJ/mol
for the reaction you show. Then
(105,500/8.314*298) = lnK and i get a huge number for K. Somethng
like 3.1E18