HCl + H2O2 + FeCl2 = H2O + FeCl3

HCl (hydrogen chloride) + H_2O_2 (hydrogen peroxide) + FeCl_2 (iron(II) chloride) ⟶ H_2O (water) + FeCl_3 (iron(III) chloride)

Balance the chemical equation algebraically: HCl + H_2O_2 + FeCl_2 ⟶ H_2O + FeCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 H_2O_2 + c_3 FeCl_2 ⟶ c_4 H_2O + c_5 FeCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, O and Fe: Cl: | c_1 + 2 c_3 = 3 c_5 H: | c_1 + 2 c_2 = 2 c_4 O: | 2 c_2 = c_4 Fe: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + H_2O_2 + 2 FeCl_2 ⟶ 2 H_2O + 2 FeCl_3

+ + ⟶ +

hydrogen chloride + hydrogen peroxide + iron(II) chloride ⟶ water + iron(III) chloride

| hydrogen chloride | hydrogen peroxide | iron(II) chloride | water | iron(III) chloride molecular free energy | -95.3 kJ/mol | -120.4 kJ/mol | -302.3 kJ/mol | -237.1 kJ/mol | -334 kJ/mol total free energy | -190.6 kJ/mol | -120.4 kJ/mol | -604.6 kJ/mol | -474.2 kJ/mol | -668 kJ/mol | G_initial = -915.6 kJ/mol | | | G_final = -1142 kJ/mol | ΔG_rxn^0 | -1142 kJ/mol - -915.6 kJ/mol = -226.6 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: HCl + H_2O_2 + FeCl_2 ⟶ H_2O + 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: 2 HCl + H_2O_2 + 2 FeCl_2 ⟶ 2 H_2O + 2 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 | 2 | -2 H_2O_2 | 1 | -1 FeCl_2 | 2 | -2 H_2O | 2 | 2 FeCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 2 | -2 | ([HCl])^(-2) H_2O_2 | 1 | -1 | ([H2O2])^(-1) FeCl_2 | 2 | -2 | ([FeCl2])^(-2) H_2O | 2 | 2 | ([H2O])^2 FeCl_3 | 2 | 2 | ([FeCl3])^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 = ([HCl])^(-2) ([H2O2])^(-1) ([FeCl2])^(-2) ([H2O])^2 ([FeCl3])^2 = (([H2O])^2 ([FeCl3])^2)/(([HCl])^2 [H2O2] ([FeCl2])^2)

Construct the rate of reaction expression for: HCl + H_2O_2 + FeCl_2 ⟶ H_2O + 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: 2 HCl + H_2O_2 + 2 FeCl_2 ⟶ 2 H_2O + 2 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 | 2 | -2 H_2O_2 | 1 | -1 FeCl_2 | 2 | -2 H_2O | 2 | 2 FeCl_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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) FeCl_2 | 2 | -2 | -1/2 (Δ[FeCl2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) FeCl_3 | 2 | 2 | 1/2 (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 = -1/2 (Δ[HCl])/(Δt) = -(Δ[H2O2])/(Δt) = -1/2 (Δ[FeCl2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[FeCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | hydrogen peroxide | iron(II) chloride | water | iron(III) chloride formula | HCl | H_2O_2 | FeCl_2 | H_2O | FeCl_3 Hill formula | ClH | H_2O_2 | Cl_2Fe | H_2O | Cl_3Fe name | hydrogen chloride | hydrogen peroxide | iron(II) chloride | water | iron(III) chloride IUPAC name | hydrogen chloride | hydrogen peroxide | dichloroiron | water | trichloroiron