Al + HClO3 = H2O + AlCl3 + Al(ClO3)3

Al aluminum + HClO3 ⟶ H_2O water + AlCl_3 aluminum chloride + AlCl_3O_9 aluminum chlorate nonahydrate

Balance the chemical equation algebraically: Al + HClO3 ⟶ H_2O + AlCl_3 + AlCl_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 HClO3 ⟶ c_3 H_2O + c_4 AlCl_3 + c_5 AlCl_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, H, Cl and O: Al: | c_1 = c_4 + c_5 H: | c_2 = 2 c_3 Cl: | c_2 = 3 c_4 + 3 c_5 O: | 3 c_2 = c_3 + 9 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 18 c_3 = 9 c_4 = 1 c_5 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Al + 18 HClO3 ⟶ 9 H_2O + AlCl_3 + 5 AlCl_3O_9

+ HClO3 ⟶ + +

aluminum + HClO3 ⟶ water + aluminum chloride + aluminum chlorate nonahydrate

Construct the equilibrium constant, K, expression for: Al + HClO3 ⟶ H_2O + AlCl_3 + AlCl_3O_9 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: 6 Al + 18 HClO3 ⟶ 9 H_2O + AlCl_3 + 5 AlCl_3O_9 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 Al | 6 | -6 HClO3 | 18 | -18 H_2O | 9 | 9 AlCl_3 | 1 | 1 AlCl_3O_9 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 6 | -6 | ([Al])^(-6) HClO3 | 18 | -18 | ([HClO3])^(-18) H_2O | 9 | 9 | ([H2O])^9 AlCl_3 | 1 | 1 | [AlCl3] AlCl_3O_9 | 5 | 5 | ([AlCl3O9])^5 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 = ([Al])^(-6) ([HClO3])^(-18) ([H2O])^9 [AlCl3] ([AlCl3O9])^5 = (([H2O])^9 [AlCl3] ([AlCl3O9])^5)/(([Al])^6 ([HClO3])^18)

Construct the rate of reaction expression for: Al + HClO3 ⟶ H_2O + AlCl_3 + AlCl_3O_9 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: 6 Al + 18 HClO3 ⟶ 9 H_2O + AlCl_3 + 5 AlCl_3O_9 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 Al | 6 | -6 HClO3 | 18 | -18 H_2O | 9 | 9 AlCl_3 | 1 | 1 AlCl_3O_9 | 5 | 5 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 Al | 6 | -6 | -1/6 (Δ[Al])/(Δt) HClO3 | 18 | -18 | -1/18 (Δ[HClO3])/(Δt) H_2O | 9 | 9 | 1/9 (Δ[H2O])/(Δt) AlCl_3 | 1 | 1 | (Δ[AlCl3])/(Δt) AlCl_3O_9 | 5 | 5 | 1/5 (Δ[AlCl3O9])/(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 = -1/6 (Δ[Al])/(Δt) = -1/18 (Δ[HClO3])/(Δt) = 1/9 (Δ[H2O])/(Δt) = (Δ[AlCl3])/(Δt) = 1/5 (Δ[AlCl3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | HClO3 | water | aluminum chloride | aluminum chlorate nonahydrate formula | Al | HClO3 | H_2O | AlCl_3 | AlCl_3O_9 name | aluminum | | water | aluminum chloride | aluminum chlorate nonahydrate IUPAC name | aluminum | | water | trichloroalumane | aluminum(+3) cation trichlorate