Question

Need help finding K

When the oxide of generic metal M is heated at 25.0 degree C, only a negligible amount of M is produced. MO_2(s) rightleftharpoons M(s) + O_2(g) Delta CO_2=291.4 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). What is the thermodynamic equilbrium constant for the coupled reaction? K =

Answer 1

The general equation for this would be the following:
$\dpi{100} \small \Delta G$ = $\dpi{100} \small \Delta G$ ° + RTlnK

Now, the question said that the reaction once coupled with graphite, the reaction becomes spontaneous, this means that $\dpi{100} \small \Delta G$ = 0, so the above equation will be reduced like this:

EDITED

0 = $\dpi{100} \small \Delta G$ ° + RTlnK ---> From here we can solve for K so:
$\dpi{100} \small \Delta G$ ° = -RTlnK
K = exp (-$\dpi{100} \small \Delta G$°/RT)

So replacing now the values we have:

K = exp(-291400 / 8.3144*298)
K = 8.37x10^-52

Hope this helps