Question

Calculate the equilibrium constant (Kc) for the reaction 2SO2(g) + O2(g) ⇌ 2SO3(g) if at a certain temperature, the initial concentrations of SO2, O2, and SO3 are 0.1 M, 0.2 M, and 0 M, respectively. The equilibrium concentrations of SO2 and SO3 are both 0.05 M. Assume the reaction takes place in a closed system at constant pressure.

Answer 1

To calculate the equilibrium constant  Kc  for the given reaction, we first need to determine the change in concentrations of each species during the reaction. Since the reaction is balanced, we can use stoichiometry to find the changes in concentrations.Initial concentrations:[SO2] = 0.1 M[O2] = 0.2 M[SO3] = 0 MEquilibrium concentrations:[SO2] = 0.05 M[O2] = ?[SO3] = 0.05 MChange in concentrations:[SO2] = -0.05 M  since it is a reactant [O2] = ?[SO3] = +0.05 M  since it is a product From the stoichiometry of the balanced reaction, we can see that 2 moles of SO2 react with 1 mole of O2 to produce 2 moles of SO3. Therefore, the change in concentration of O2 is half the change in concentration of SO2:[O2] =  1/2  * [SO2] =  1/2  *  -0.05 M  = -0.025 MNow we can find the equilibrium concentration of O2:[O2] = initial concentration + change in concentration[O2] = 0.2 M +  -0.025 M  = 0.175 MNow that we have the equilibrium concentrations of all species, we can calculate the equilibrium constant  Kc  using the expression:Kc = [SO3]^2 /  [SO2]^2 * [O2] Plugging in the equilibrium concentrations:Kc =  0.05 ^2 /   0.05 ^2 *  0.175  Kc = 0.0025 /  0.0025 * 0.175 Kc = 0.0025 / 0.0004375Kc  5.71Therefore, the equilibrium constant  Kc  for the given reaction is approximately 5.71.