Final answer:
To calculate the equilibrium constant (Kc) for the reaction 2SO₃(g) ⇌ 2SO₂(g) + O₂(g), the concentrations of the reactants and products at equilibrium are used in the Kc expression.
Step-by-step explanation:
To calculate the equilibrium constant (Kc) for the reaction 2SO₃(g) ⇌ 2SO₂(g) + O₂(g), given the amount of SO₃ and O₂ at equilibrium, we need to use the equilibrium constant expression Kc = [SO₂]^2 [O₂] / [SO₃]^2. We know that initially there was 0.980 mol of SO₃ in a 4.50 L container, which gives us an initial concentration of [SO₃] = 0.980 mol / 4.50 L = 0.218 M.
At equilibrium, 0.130 mol of O₂ is present, which translates to [O₂] = 0.130 mol / 4.50 L = 0.029 M. Since the reaction produces O₂ in half the amount to the SO₂ produced, there will be 0.260 mol of SO₂ formed (twice the amount of O₂), which means [SO₂] = 0.260 mol / 4.50 L = 0.058 M.
The change in concentration for SO3 is equivalent to the amount of O₂ formed, so the equilibrium concentration of [SO₃] is 0.218 M - 0.029 M = 0.189 M.
Plugging these values into the equilibrium expression:
Kc = ([SO₂]^2 [O₂]) / [SO₃]^2 = (0.058 M)^2 x (0.029 M) / (0.189 M)^2
Calculating this gives us:
Kc = 0.00336 / 0.0357 = ≈ 0.094
Therefore, the equilibrium constant for the reaction at this temperature is approximately 0.094.
After calculating the concentrations, Kc is found to be approximately 0.094 at the given temperature.