HCl + FeCl2 + HClO4 = H2O + Cl2 + FeCl3

HCl hydrogen chloride + FeCl_2 iron(II) chloride + HClO_4 perchloric acid ⟶ H_2O water + Cl_2 chlorine + FeCl_3 iron(III) chloride

Balance the chemical equation algebraically: HCl + FeCl_2 + HClO_4 ⟶ H_2O + Cl_2 + FeCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 FeCl_2 + c_3 HClO_4 ⟶ c_4 H_2O + c_5 Cl_2 + c_6 FeCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Fe and O: Cl: | c_1 + 2 c_2 + c_3 = 2 c_5 + 3 c_6 H: | c_1 + c_3 = 2 c_4 Fe: | c_2 = c_6 O: | 4 c_3 = c_4 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 = 7 c_3 = 1 c_4 = 4 c_5 = 4 - c_2/2 c_6 = c_2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 4 and solve for the remaining coefficients: c_1 = 7 c_2 = 4 c_3 = 1 c_4 = 4 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 HCl + 4 FeCl_2 + HClO_4 ⟶ 4 H_2O + 2 Cl_2 + 4 FeCl_3

+ + ⟶ + +

hydrogen chloride + iron(II) chloride + perchloric acid ⟶ water + chlorine + iron(III) chloride

Construct the equilibrium constant, K, expression for: HCl + FeCl_2 + HClO_4 ⟶ H_2O + Cl_2 + FeCl_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: 7 HCl + 4 FeCl_2 + HClO_4 ⟶ 4 H_2O + 2 Cl_2 + 4 FeCl_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 HCl | 7 | -7 FeCl_2 | 4 | -4 HClO_4 | 1 | -1 H_2O | 4 | 4 Cl_2 | 2 | 2 FeCl_3 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 7 | -7 | ([HCl])^(-7) FeCl_2 | 4 | -4 | ([FeCl2])^(-4) HClO_4 | 1 | -1 | ([HClO4])^(-1) H_2O | 4 | 4 | ([H2O])^4 Cl_2 | 2 | 2 | ([Cl2])^2 FeCl_3 | 4 | 4 | ([FeCl3])^4 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 = ([HCl])^(-7) ([FeCl2])^(-4) ([HClO4])^(-1) ([H2O])^4 ([Cl2])^2 ([FeCl3])^4 = (([H2O])^4 ([Cl2])^2 ([FeCl3])^4)/(([HCl])^7 ([FeCl2])^4 [HClO4])

Construct the rate of reaction expression for: HCl + FeCl_2 + HClO_4 ⟶ H_2O + Cl_2 + FeCl_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: 7 HCl + 4 FeCl_2 + HClO_4 ⟶ 4 H_2O + 2 Cl_2 + 4 FeCl_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 HCl | 7 | -7 FeCl_2 | 4 | -4 HClO_4 | 1 | -1 H_2O | 4 | 4 Cl_2 | 2 | 2 FeCl_3 | 4 | 4 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 HCl | 7 | -7 | -1/7 (Δ[HCl])/(Δt) FeCl_2 | 4 | -4 | -1/4 (Δ[FeCl2])/(Δt) HClO_4 | 1 | -1 | -(Δ[HClO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Cl_2 | 2 | 2 | 1/2 (Δ[Cl2])/(Δt) FeCl_3 | 4 | 4 | 1/4 (Δ[FeCl3])/(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 = -1/7 (Δ[HCl])/(Δt) = -1/4 (Δ[FeCl2])/(Δt) = -(Δ[HClO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[Cl2])/(Δt) = 1/4 (Δ[FeCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | iron(II) chloride | perchloric acid | water | chlorine | iron(III) chloride formula | HCl | FeCl_2 | HClO_4 | H_2O | Cl_2 | FeCl_3 Hill formula | ClH | Cl_2Fe | ClHO_4 | H_2O | Cl_2 | Cl_3Fe name | hydrogen chloride | iron(II) chloride | perchloric acid | water | chlorine | iron(III) chloride IUPAC name | hydrogen chloride | dichloroiron | perchloric acid | water | molecular chlorine | trichloroiron