O2 + SO2 + CaCO3 = CO2 + CaSO4

O_2 oxygen + SO_2 sulfur dioxide + CaCO_3 calcium carbonate ⟶ CO_2 carbon dioxide + CaSO_4 calcium sulfate

Balance the chemical equation algebraically: O_2 + SO_2 + CaCO_3 ⟶ CO_2 + CaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 SO_2 + c_3 CaCO_3 ⟶ c_4 CO_2 + c_5 CaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S, C and Ca: O: | 2 c_1 + 2 c_2 + 3 c_3 = 2 c_4 + 4 c_5 S: | c_2 = c_5 C: | c_3 = c_4 Ca: | c_3 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + 2 SO_2 + 2 CaCO_3 ⟶ 2 CO_2 + 2 CaSO_4

+ + ⟶ +

oxygen + sulfur dioxide + calcium carbonate ⟶ carbon dioxide + calcium sulfate

Construct the equilibrium constant, K, expression for: O_2 + SO_2 + CaCO_3 ⟶ CO_2 + CaSO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: O_2 + 2 SO_2 + 2 CaCO_3 ⟶ 2 CO_2 + 2 CaSO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i O_2 | 1 | -1 SO_2 | 2 | -2 CaCO_3 | 2 | -2 CO_2 | 2 | 2 CaSO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) SO_2 | 2 | -2 | ([SO2])^(-2) CaCO_3 | 2 | -2 | ([CaCO3])^(-2) CO_2 | 2 | 2 | ([CO2])^2 CaSO_4 | 2 | 2 | ([CaSO4])^2 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([O2])^(-1) ([SO2])^(-2) ([CaCO3])^(-2) ([CO2])^2 ([CaSO4])^2 = (([CO2])^2 ([CaSO4])^2)/([O2] ([SO2])^2 ([CaCO3])^2)

Construct the rate of reaction expression for: O_2 + SO_2 + CaCO_3 ⟶ CO_2 + CaSO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: O_2 + 2 SO_2 + 2 CaCO_3 ⟶ 2 CO_2 + 2 CaSO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i O_2 | 1 | -1 SO_2 | 2 | -2 CaCO_3 | 2 | -2 CO_2 | 2 | 2 CaSO_4 | 2 | 2 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term O_2 | 1 | -1 | -(Δ[O2])/(Δt) SO_2 | 2 | -2 | -1/2 (Δ[SO2])/(Δt) CaCO_3 | 2 | -2 | -1/2 (Δ[CaCO3])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) CaSO_4 | 2 | 2 | 1/2 (Δ[CaSO4])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -(Δ[O2])/(Δt) = -1/2 (Δ[SO2])/(Δt) = -1/2 (Δ[CaCO3])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[CaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | sulfur dioxide | calcium carbonate | carbon dioxide | calcium sulfate formula | O_2 | SO_2 | CaCO_3 | CO_2 | CaSO_4 Hill formula | O_2 | O_2S | CCaO_3 | CO_2 | CaO_4S name | oxygen | sulfur dioxide | calcium carbonate | carbon dioxide | calcium sulfate IUPAC name | molecular oxygen | sulfur dioxide | calcium carbonate | carbon dioxide | calcium sulfate