H2O + FeCl3 = HCl + Fe2O3

H_2O water + FeCl_3 iron(III) chloride ⟶ HCl hydrogen chloride + Fe_2O_3 iron(III) oxide

Balance the chemical equation algebraically: H_2O + FeCl_3 ⟶ HCl + Fe_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 FeCl_3 ⟶ c_3 HCl + c_4 Fe_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl and Fe: H: | 2 c_1 = c_3 O: | c_1 = 3 c_4 Cl: | 3 c_2 = c_3 Fe: | c_2 = 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 FeCl_3 ⟶ 6 HCl + Fe_2O_3

+ ⟶ +

water + iron(III) chloride ⟶ hydrogen chloride + iron(III) oxide

| water | iron(III) chloride | hydrogen chloride | iron(III) oxide molecular enthalpy | -285.8 kJ/mol | -399.5 kJ/mol | -92.3 kJ/mol | -826 kJ/mol total enthalpy | -857.5 kJ/mol | -799 kJ/mol | -553.8 kJ/mol | -826 kJ/mol | H_initial = -1656 kJ/mol | | H_final = -1380 kJ/mol | ΔH_rxn^0 | -1380 kJ/mol - -1656 kJ/mol = 276.7 kJ/mol (endothermic) | | |

| water | iron(III) chloride | hydrogen chloride | iron(III) oxide molecular free energy | -237.1 kJ/mol | -334 kJ/mol | -95.3 kJ/mol | -742.2 kJ/mol total free energy | -711.3 kJ/mol | -668 kJ/mol | -571.8 kJ/mol | -742.2 kJ/mol | G_initial = -1379 kJ/mol | | G_final = -1314 kJ/mol | ΔG_rxn^0 | -1314 kJ/mol - -1379 kJ/mol = 65.3 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: H_2O + FeCl_3 ⟶ HCl + 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: 3 H_2O + 2 FeCl_3 ⟶ 6 HCl + 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 H_2O | 3 | -3 FeCl_3 | 2 | -2 HCl | 6 | 6 Fe_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) FeCl_3 | 2 | -2 | ([FeCl3])^(-2) HCl | 6 | 6 | ([HCl])^6 Fe_2O_3 | 1 | 1 | [Fe2O3] 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])^(-3) ([FeCl3])^(-2) ([HCl])^6 [Fe2O3] = (([HCl])^6 [Fe2O3])/(([H2O])^3 ([FeCl3])^2)

Construct the rate of reaction expression for: H_2O + FeCl_3 ⟶ HCl + 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: 3 H_2O + 2 FeCl_3 ⟶ 6 HCl + 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 H_2O | 3 | -3 FeCl_3 | 2 | -2 HCl | 6 | 6 Fe_2O_3 | 1 | 1 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) FeCl_3 | 2 | -2 | -1/2 (Δ[FeCl3])/(Δt) HCl | 6 | 6 | 1/6 (Δ[HCl])/(Δt) Fe_2O_3 | 1 | 1 | (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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[FeCl3])/(Δt) = 1/6 (Δ[HCl])/(Δt) = (Δ[Fe2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | iron(III) chloride | hydrogen chloride | iron(III) oxide formula | H_2O | FeCl_3 | HCl | Fe_2O_3 Hill formula | H_2O | Cl_3Fe | ClH | Fe_2O_3 name | water | iron(III) chloride | hydrogen chloride | iron(III) oxide IUPAC name | water | trichloroiron | hydrogen chloride |

| water | iron(III) chloride | hydrogen chloride | iron(III) oxide molar mass | 18.015 g/mol | 162.2 g/mol | 36.46 g/mol | 159.69 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 0 °C | 304 °C | -114.17 °C | 1565 °C boiling point | 99.9839 °C | | -85 °C | density | 1 g/cm^3 | | 0.00149 g/cm^3 (at 25 °C) | 5.26 g/cm^3 solubility in water | | | miscible | insoluble surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | | | odorless