I'm stuck...that is i believe I've come to an impossible answer:
I need to calculate the equilibrium constant
4Fe(s) + 3O2(g) --> 2Fe2O3(s)
First off: Delta G G Fe(s) = 0, G O2(g) = 0, G Fe2O3(s) = -741 (x2)
-741 (2) - 0 = -1480 = delta G of reaction
at equilibrium:
0 = (delta G rxn) + RT (lnk) or lnk = -(delta G rxn) / RT
so, lnk = 1480 / 2.478 = 598 = lnk
k = e^598 = Impossible? This would be an humongous number so I think I went astray somewhere.
Any help?
It seems like you've made a mistake in your calculation. Let's go through the steps together to find the correct equilibrium constant (K) for the given reaction.
Step 1: Calculate the change in Gibbs free energy (ΔG) for the reaction.
ΔG = Σ(ΔG of products) - Σ(ΔG of reactants)
ΔG = (2 * -741 kJ/mol) - (0 + 0)
ΔG = -1482 kJ/mol
Note that you multiplied the ΔG value of Fe2O3 by 2, but since the stoichiometric coefficient in the balanced equation is already 2, you should consider the value as it is.
Step 2: Convert ΔG to ΔG in J/mol.
ΔG = -1482 kJ/mol * 1000 J/1 kJ
ΔG = -1,482,000 J/mol
Step 3: Calculate the equilibrium constant (K) using the equation:
ln(K) = -ΔG / (RT)
Given:
R = gas constant = 8.314 J/(mol·K)
T = temperature in Kelvin (make sure to use the same units as in ΔG)
Let's assume the temperature is 298 K.
ln(K) = -1,482,000 J/mol / (8.314 J/(mol·K) * 298 K)
ln(K) = -1,482,000 J/mol / 2474.072 J/mol
ln(K) ≈ -598.816
Step 4: Solve for K using the natural logarithm (ln).
K = e^(-598.816)
K ≈ 2.25 * 10^(-260)
So, the correct equilibrium constant for the reaction is approximately 2.25 x 10^(-260). It is indeed a very small number, which indicates that the reaction strongly favors the reactants.
Please double-check your calculations and make sure you are using the correct values for ΔG and temperature.