H2O + AlCl3 = HCl + Al2O3

H_2O water + AlCl_3 aluminum chloride ⟶ HCl hydrogen chloride + Al_2O_3 aluminum oxide

Balance the chemical equation algebraically: H_2O + AlCl_3 ⟶ HCl + Al_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AlCl_3 ⟶ c_3 HCl + c_4 Al_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al and Cl: H: | 2 c_1 = c_3 O: | c_1 = 3 c_4 Al: | c_2 = 2 c_4 Cl: | 3 c_2 = c_3 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 AlCl_3 ⟶ 6 HCl + Al_2O_3

+ ⟶ +

water + aluminum chloride ⟶ hydrogen chloride + aluminum oxide

| water | aluminum chloride | hydrogen chloride | aluminum oxide molecular enthalpy | -285.8 kJ/mol | -704.2 kJ/mol | -92.3 kJ/mol | -1676 kJ/mol total enthalpy | -857.5 kJ/mol | -1408 kJ/mol | -553.8 kJ/mol | -1676 kJ/mol | H_initial = -2266 kJ/mol | | H_final = -2230 kJ/mol | ΔH_rxn^0 | -2230 kJ/mol - -2266 kJ/mol = 36.09 kJ/mol (endothermic) | | |

| water | aluminum chloride | hydrogen chloride | aluminum oxide molecular free energy | -237.1 kJ/mol | -628.8 kJ/mol | -95.3 kJ/mol | -1582 kJ/mol total free energy | -711.3 kJ/mol | -1258 kJ/mol | -571.8 kJ/mol | -1582 kJ/mol | G_initial = -1969 kJ/mol | | G_final = -2154 kJ/mol | ΔG_rxn^0 | -2154 kJ/mol - -1969 kJ/mol = -184.9 kJ/mol (exergonic) | | |

| water | aluminum chloride | hydrogen chloride | aluminum oxide molecular entropy | 69.91 J/(mol K) | 111 J/(mol K) | 187 J/(mol K) | 51 J/(mol K) total entropy | 209.7 J/(mol K) | 222 J/(mol K) | 1122 J/(mol K) | 51 J/(mol K) | S_initial = 431.7 J/(mol K) | | S_final = 1173 J/(mol K) | ΔS_rxn^0 | 1173 J/(mol K) - 431.7 J/(mol K) = 741.3 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2O + AlCl_3 ⟶ HCl + Al_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 AlCl_3 ⟶ 6 HCl + Al_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 AlCl_3 | 2 | -2 HCl | 6 | 6 Al_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) AlCl_3 | 2 | -2 | ([AlCl3])^(-2) HCl | 6 | 6 | ([HCl])^6 Al_2O_3 | 1 | 1 | [Al2O3] 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) ([AlCl3])^(-2) ([HCl])^6 [Al2O3] = (([HCl])^6 [Al2O3])/(([H2O])^3 ([AlCl3])^2)

Construct the rate of reaction expression for: H_2O + AlCl_3 ⟶ HCl + Al_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 AlCl_3 ⟶ 6 HCl + Al_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 AlCl_3 | 2 | -2 HCl | 6 | 6 Al_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) AlCl_3 | 2 | -2 | -1/2 (Δ[AlCl3])/(Δt) HCl | 6 | 6 | 1/6 (Δ[HCl])/(Δt) Al_2O_3 | 1 | 1 | (Δ[Al2O3])/(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[AlCl3])/(Δt) = 1/6 (Δ[HCl])/(Δt) = (Δ[Al2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | aluminum chloride | hydrogen chloride | aluminum oxide formula | H_2O | AlCl_3 | HCl | Al_2O_3 Hill formula | H_2O | AlCl_3 | ClH | Al_2O_3 name | water | aluminum chloride | hydrogen chloride | aluminum oxide IUPAC name | water | trichloroalumane | hydrogen chloride | dialuminum;oxygen(2-)

| water | aluminum chloride | hydrogen chloride | aluminum oxide molar mass | 18.015 g/mol | 133.3 g/mol | 36.46 g/mol | 101.96 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 0 °C | 190 °C | -114.17 °C | 2040 °C boiling point | 99.9839 °C | | -85 °C | density | 1 g/cm^3 | | 0.00149 g/cm^3 (at 25 °C) | solubility in water | | | miscible | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | | | odorless