Final answer:
The Kc value of 53 at 550°C is for the reaction of sulfur dioxide with oxygen to form sulfur trioxide. To find the overall equilibrium constant at 25°C for the synthesis of sulfuric acid, the individual constants for the two steps must be combined.
Step-by-step explanation:
The chemical equilibrium between sulfur dioxide and oxygen to form sulfur trioxide (2SO₂ (g) + O₂ (g) → 2SO₃ (g)) at 550°C has a Kc value of 53. This equation represents the second step in the industrial synthesis of sulfuric acid. To calculate the equilibrium constant for the overall synthesis reaction at 25°C, you need the equilibrium constants for both individual steps at that temperature. These values are typically multiplied when the sequential reactions have a common intermediate (SO₂), as is the case here.
Additionally, if given concentrations for the reactants and products at equilibrium, one could calculate Kc by using the equation Kc = [SO₃]² / ([SO₂]² × [O₂]), where the brackets denote the molar concentrations of the gases. Similarly, Kp can be calculated if the partial pressures are known, taking into account the relationship between Kc and Kp, which involves the gas constant (R) and the temperature (T).