Cl2 + KOH + FeS2 = H2O + K2SO4 + KCl + K2FeO4

Cl_2 chlorine + KOH potassium hydroxide + FeS_2 pyrite ⟶ H_2O water + K_2SO_4 potassium sulfate + KCl potassium chloride + K_2FeO_4 potassium ferrate(VI)

Balance the chemical equation algebraically: Cl_2 + KOH + FeS_2 ⟶ H_2O + K_2SO_4 + KCl + K_2FeO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 KOH + c_3 FeS_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 KCl + c_7 K_2FeO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, O, Fe and S: Cl: | 2 c_1 = c_6 H: | c_2 = 2 c_4 K: | c_2 = 2 c_5 + c_6 + c_7 O: | c_2 = c_4 + 4 c_5 + 2 c_7 Fe: | c_3 = c_7 S: | 2 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 15/2 c_2 = 20 c_3 = 1 c_4 = 10 c_5 = 2 c_6 = 15 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 15 c_2 = 40 c_3 = 2 c_4 = 20 c_5 = 4 c_6 = 30 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 15 Cl_2 + 40 KOH + 2 FeS_2 ⟶ 20 H_2O + 4 K_2SO_4 + 30 KCl + 2 K_2FeO_4

+ + ⟶ + + +

chlorine + potassium hydroxide + pyrite ⟶ water + potassium sulfate + potassium chloride + potassium ferrate(VI)

Construct the equilibrium constant, K, expression for: Cl_2 + KOH + FeS_2 ⟶ H_2O + K_2SO_4 + KCl + K_2FeO_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: 15 Cl_2 + 40 KOH + 2 FeS_2 ⟶ 20 H_2O + 4 K_2SO_4 + 30 KCl + 2 K_2FeO_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 Cl_2 | 15 | -15 KOH | 40 | -40 FeS_2 | 2 | -2 H_2O | 20 | 20 K_2SO_4 | 4 | 4 KCl | 30 | 30 K_2FeO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 15 | -15 | ([Cl2])^(-15) KOH | 40 | -40 | ([KOH])^(-40) FeS_2 | 2 | -2 | ([FeS2])^(-2) H_2O | 20 | 20 | ([H2O])^20 K_2SO_4 | 4 | 4 | ([K2SO4])^4 KCl | 30 | 30 | ([KCl])^30 K_2FeO_4 | 2 | 2 | ([K2FeO4])^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 = ([Cl2])^(-15) ([KOH])^(-40) ([FeS2])^(-2) ([H2O])^20 ([K2SO4])^4 ([KCl])^30 ([K2FeO4])^2 = (([H2O])^20 ([K2SO4])^4 ([KCl])^30 ([K2FeO4])^2)/(([Cl2])^15 ([KOH])^40 ([FeS2])^2)

Construct the rate of reaction expression for: Cl_2 + KOH + FeS_2 ⟶ H_2O + K_2SO_4 + KCl + K_2FeO_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: 15 Cl_2 + 40 KOH + 2 FeS_2 ⟶ 20 H_2O + 4 K_2SO_4 + 30 KCl + 2 K_2FeO_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 Cl_2 | 15 | -15 KOH | 40 | -40 FeS_2 | 2 | -2 H_2O | 20 | 20 K_2SO_4 | 4 | 4 KCl | 30 | 30 K_2FeO_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 Cl_2 | 15 | -15 | -1/15 (Δ[Cl2])/(Δt) KOH | 40 | -40 | -1/40 (Δ[KOH])/(Δt) FeS_2 | 2 | -2 | -1/2 (Δ[FeS2])/(Δt) H_2O | 20 | 20 | 1/20 (Δ[H2O])/(Δt) K_2SO_4 | 4 | 4 | 1/4 (Δ[K2SO4])/(Δt) KCl | 30 | 30 | 1/30 (Δ[KCl])/(Δt) K_2FeO_4 | 2 | 2 | 1/2 (Δ[K2FeO4])/(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 = -1/15 (Δ[Cl2])/(Δt) = -1/40 (Δ[KOH])/(Δt) = -1/2 (Δ[FeS2])/(Δt) = 1/20 (Δ[H2O])/(Δt) = 1/4 (Δ[K2SO4])/(Δt) = 1/30 (Δ[KCl])/(Δt) = 1/2 (Δ[K2FeO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | potassium hydroxide | pyrite | water | potassium sulfate | potassium chloride | potassium ferrate(VI) formula | Cl_2 | KOH | FeS_2 | H_2O | K_2SO_4 | KCl | K_2FeO_4 Hill formula | Cl_2 | HKO | FeS_2 | H_2O | K_2O_4S | ClK | FeK_2O_4 name | chlorine | potassium hydroxide | pyrite | water | potassium sulfate | potassium chloride | potassium ferrate(VI) IUPAC name | molecular chlorine | potassium hydroxide | bis(sulfanylidene)iron | water | dipotassium sulfate | potassium chloride |