O2 + CuFeS2 = SO2 + CuO + Fe2O3

O_2 oxygen + CuFeS_2 copper(II) ferrous sulfide ⟶ SO_2 sulfur dioxide + CuO cupric oxide + Fe_2O_3 iron(III) oxide

Balance the chemical equation algebraically: O_2 + CuFeS_2 ⟶ SO_2 + CuO + Fe_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 CuFeS_2 ⟶ c_3 SO_2 + c_4 CuO + c_5 Fe_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Cu, Fe and S: O: | 2 c_1 = 2 c_3 + c_4 + 3 c_5 Cu: | c_2 = c_4 Fe: | c_2 = 2 c_5 S: | 2 c_2 = c_3 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 13/2 c_2 = 2 c_3 = 4 c_4 = 2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 13 c_2 = 4 c_3 = 8 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 13 O_2 + 4 CuFeS_2 ⟶ 8 SO_2 + 4 CuO + 2 Fe_2O_3

+ CuFeS_2 ⟶ + +

oxygen + copper(II) ferrous sulfide ⟶ sulfur dioxide + cupric oxide + iron(III) oxide

Construct the equilibrium constant, K, expression for: O_2 + CuFeS_2 ⟶ SO_2 + CuO + Fe_2O_3 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: 13 O_2 + 4 CuFeS_2 ⟶ 8 SO_2 + 4 CuO + 2 Fe_2O_3 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 | 13 | -13 CuFeS_2 | 4 | -4 SO_2 | 8 | 8 CuO | 4 | 4 Fe_2O_3 | 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 | 13 | -13 | ([O2])^(-13) CuFeS_2 | 4 | -4 | ([CuFeS2])^(-4) SO_2 | 8 | 8 | ([SO2])^8 CuO | 4 | 4 | ([CuO])^4 Fe_2O_3 | 2 | 2 | ([Fe2O3])^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])^(-13) ([CuFeS2])^(-4) ([SO2])^8 ([CuO])^4 ([Fe2O3])^2 = (([SO2])^8 ([CuO])^4 ([Fe2O3])^2)/(([O2])^13 ([CuFeS2])^4)

Construct the rate of reaction expression for: O_2 + CuFeS_2 ⟶ SO_2 + CuO + Fe_2O_3 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: 13 O_2 + 4 CuFeS_2 ⟶ 8 SO_2 + 4 CuO + 2 Fe_2O_3 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 | 13 | -13 CuFeS_2 | 4 | -4 SO_2 | 8 | 8 CuO | 4 | 4 Fe_2O_3 | 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 | 13 | -13 | -1/13 (Δ[O2])/(Δt) CuFeS_2 | 4 | -4 | -1/4 (Δ[CuFeS2])/(Δt) SO_2 | 8 | 8 | 1/8 (Δ[SO2])/(Δt) CuO | 4 | 4 | 1/4 (Δ[CuO])/(Δt) Fe_2O_3 | 2 | 2 | 1/2 (Δ[Fe2O3])/(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 = -1/13 (Δ[O2])/(Δt) = -1/4 (Δ[CuFeS2])/(Δt) = 1/8 (Δ[SO2])/(Δt) = 1/4 (Δ[CuO])/(Δt) = 1/2 (Δ[Fe2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | copper(II) ferrous sulfide | sulfur dioxide | cupric oxide | iron(III) oxide formula | O_2 | CuFeS_2 | SO_2 | CuO | Fe_2O_3 Hill formula | O_2 | CuFeS_2 | O_2S | CuO | Fe_2O_3 name | oxygen | copper(II) ferrous sulfide | sulfur dioxide | cupric oxide | iron(III) oxide IUPAC name | molecular oxygen | | sulfur dioxide | |