Sulfur trioxide, a precursor of sulfuric acid, is prepared industrially using the contact process by passing sulfur dioxide and oxygen over a hot catalyst:
2SO2(g) + O2 (g) <--> 2SO3 (g)
Using a table of thermodynamic data, estimate the temperature at which the reaction begins to favor the formation of products at equilibrium. Round your answer to 3 significant digits.
To determine the temperature at which the reaction begins to favor the formation of products at equilibrium, we need to calculate the equilibrium constant (K) for the reaction using the equation:
ΔG° = -RT ln(K)
First, we need to calculate the standard Gibbs free energy change (ΔG°) for the reaction using the following equation:
ΔG° = ΣnG°(products) - ΣnG°(reactants)
Using standard Gibbs free energy of formation values from tables:
ΔG° = 2(-396.2 kJ/mol) - 0 kJ/mol - (2(-296.8 kJ/mol)) = -198.8 kJ/mol
Now, we convert the ΔG° to joules:
ΔG° = -198.8 kJ/mol * 1000 J/kJ = -198,800 J/mol
Now, we can rearrange the equation to solve for the equilibrium constant (K):
K = e^(-ΔG°/RT)
We don't have the exact value for R (gas constant), but it's usually taken as 8.314 J/(mol*K). We can assume a temperature of 298 K to get an estimate.
K = e^(-(-198,800 J/mol)/(8.314 J/(mol*K) * 298 K))
K ≈ e^(252.93) ≈ 3.4 x 10^109
So, at a temperature of around 298 K, the reaction begins to favor the formation of products at equilibrium.