When the oxide of generic metal M is heated at 25.0 °C, only a negligible amount of M is produced.

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
Check that carefully.

yes it is correct! Thanks so much! You are the best!!!!!

K=e raised to -(-106.4 kj/mol)/(8.314e-3kj/mol*298k)

K=4.476e18 is what I got.

I keep getting the equation wrong!

my deltaGf was dGf=290.4kJ/mol

i got K=1.69e18 as my answer and it was correct.
still getting the equation wrong though :/

1: Set all the delta g's for solids equal to 0

2:Find thr delta g for the gases.
3:Find the delta g for the second equation.
4:Add the delta g's for the 2 questions together.
5: Solve for the value of Q using the equation
-Delta G not =RTLnQ

COMBINE THE 2 EQUATIONS TOGETHER PEOPLE!

MO2 + C <-> CO2 + M

Original deltaG=288.9

deltaG(system)=deltaG[CO2]+deltaG[M]-deltaG[MO2]-deltaG[C]

look up deltaG value from table for CO2=-394.4

DeltaG for a solid is almost always zero (C)

So -394.4+288.9=deltaGsystem

then

K=e^((deltaGsystem)/((8.314/1000)*298)))

ert5y547

To determine the thermodynamic equilibrium constant for the coupled reaction, you need to use the relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant (K).

The standard Gibbs free energy change (ΔG°) is related to the equilibrium constant (K) by the equation:

ΔG° = -RTln(K)

Where:
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (K)
- ln represents the natural logarithm

In this case, the given standard Gibbs free energy change (ΔG°) is 288.9 kJ/mol, but we need to convert it to joules per mole:

ΔG° = 288.9 kJ/mol × 1000 J/1 kJ = 288,900 J/mol

Now, let's assume the equilibrium constant for the coupled reaction is K.

Substituting the values into the equation, we have:

288,900 J/mol = -8.314 J/(mol·K) × T × ln(K)

To find the equilibrium constant K, you'll need to know the temperature (T) at which the reaction is taking place. Once you have the temperature, you can rearrange the equation to solve for K:

K = e^(-ΔG° / (RT))

where e is the base of the natural logarithm (approximately 2.71828).

Make sure you use the appropriate units for temperature (Kelvin) and gas constant (J/(mol·K)).

If you provide the temperature (in Kelvin) at which the reaction is taking place, I can help you calculate the equilibrium constant (K) correctly.