H2O + SO2 + FeCl3 = H2SO4 + HCl + FeCl2

H_2O water + SO_2 sulfur dioxide + FeCl_3 iron(III) chloride ⟶ H_2SO_4 sulfuric acid + HCl hydrogen chloride + FeCl_2 iron(II) chloride

Balance the chemical equation algebraically: H_2O + SO_2 + FeCl_3 ⟶ H_2SO_4 + HCl + FeCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 FeCl_3 ⟶ c_4 H_2SO_4 + c_5 HCl + c_6 FeCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl and Fe: H: | 2 c_1 = 2 c_4 + c_5 O: | c_1 + 2 c_2 = 4 c_4 S: | c_2 = c_4 Cl: | 3 c_3 = c_5 + 2 c_6 Fe: | c_3 = c_6 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 = 1 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + SO_2 + 2 FeCl_3 ⟶ H_2SO_4 + 2 HCl + 2 FeCl_2

+ + ⟶ + +

water + sulfur dioxide + iron(III) chloride ⟶ sulfuric acid + hydrogen chloride + iron(II) chloride

| water | sulfur dioxide | iron(III) chloride | sulfuric acid | hydrogen chloride | iron(II) chloride molecular enthalpy | -285.8 kJ/mol | -296.8 kJ/mol | -399.5 kJ/mol | -814 kJ/mol | -92.3 kJ/mol | -341.8 kJ/mol total enthalpy | -571.7 kJ/mol | -296.8 kJ/mol | -799 kJ/mol | -814 kJ/mol | -184.6 kJ/mol | -683.6 kJ/mol | H_initial = -1667 kJ/mol | | | H_final = -1682 kJ/mol | | ΔH_rxn^0 | -1682 kJ/mol - -1667 kJ/mol = -14.74 kJ/mol (exothermic) | | | | |

| water | sulfur dioxide | iron(III) chloride | sulfuric acid | hydrogen chloride | iron(II) chloride molecular free energy | -237.1 kJ/mol | -300.1 kJ/mol | -334 kJ/mol | -690 kJ/mol | -95.3 kJ/mol | -302.3 kJ/mol total free energy | -474.2 kJ/mol | -300.1 kJ/mol | -668 kJ/mol | -690 kJ/mol | -190.6 kJ/mol | -604.6 kJ/mol | G_initial = -1442 kJ/mol | | | G_final = -1485 kJ/mol | | ΔG_rxn^0 | -1485 kJ/mol - -1442 kJ/mol = -42.9 kJ/mol (exergonic) | | | | |

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + FeCl_3 ⟶ H_2SO_4 + HCl + FeCl_2 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 H_2O + SO_2 + 2 FeCl_3 ⟶ H_2SO_4 + 2 HCl + 2 FeCl_2 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 H_2O | 2 | -2 SO_2 | 1 | -1 FeCl_3 | 2 | -2 H_2SO_4 | 1 | 1 HCl | 2 | 2 FeCl_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) SO_2 | 1 | -1 | ([SO2])^(-1) FeCl_3 | 2 | -2 | ([FeCl3])^(-2) H_2SO_4 | 1 | 1 | [H2SO4] HCl | 2 | 2 | ([HCl])^2 FeCl_2 | 2 | 2 | ([FeCl2])^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 = ([H2O])^(-2) ([SO2])^(-1) ([FeCl3])^(-2) [H2SO4] ([HCl])^2 ([FeCl2])^2 = ([H2SO4] ([HCl])^2 ([FeCl2])^2)/(([H2O])^2 [SO2] ([FeCl3])^2)

Construct the rate of reaction expression for: H_2O + SO_2 + FeCl_3 ⟶ H_2SO_4 + HCl + FeCl_2 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 H_2O + SO_2 + 2 FeCl_3 ⟶ H_2SO_4 + 2 HCl + 2 FeCl_2 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 H_2O | 2 | -2 SO_2 | 1 | -1 FeCl_3 | 2 | -2 H_2SO_4 | 1 | 1 HCl | 2 | 2 FeCl_2 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) FeCl_3 | 2 | -2 | -1/2 (Δ[FeCl3])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) FeCl_2 | 2 | 2 | 1/2 (Δ[FeCl2])/(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[H2O])/(Δt) = -(Δ[SO2])/(Δt) = -1/2 (Δ[FeCl3])/(Δt) = (Δ[H2SO4])/(Δt) = 1/2 (Δ[HCl])/(Δt) = 1/2 (Δ[FeCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | iron(III) chloride | sulfuric acid | hydrogen chloride | iron(II) chloride formula | H_2O | SO_2 | FeCl_3 | H_2SO_4 | HCl | FeCl_2 Hill formula | H_2O | O_2S | Cl_3Fe | H_2O_4S | ClH | Cl_2Fe name | water | sulfur dioxide | iron(III) chloride | sulfuric acid | hydrogen chloride | iron(II) chloride IUPAC name | water | sulfur dioxide | trichloroiron | sulfuric acid | hydrogen chloride | dichloroiron