HCl + Al(OH)3 = H2O + AlCl3

HCl (hydrogen chloride) + Al(OH)_3 (aluminum hydroxide) ⟶ H_2O (water) + AlCl_3 (aluminum chloride)

Balance the chemical equation algebraically: HCl + Al(OH)_3 ⟶ H_2O + AlCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Al(OH)_3 ⟶ c_3 H_2O + c_4 AlCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Al and O: Cl: | c_1 = 3 c_4 H: | c_1 + 3 c_2 = 2 c_3 Al: | c_2 = c_4 O: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 HCl + Al(OH)_3 ⟶ 3 H_2O + AlCl_3

+ ⟶ +

hydrogen chloride + aluminum hydroxide ⟶ water + aluminum chloride

Construct the equilibrium constant, K, expression for: HCl + Al(OH)_3 ⟶ H_2O + AlCl_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 HCl + Al(OH)_3 ⟶ 3 H_2O + AlCl_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 | 3 | -3 Al(OH)_3 | 1 | -1 H_2O | 3 | 3 AlCl_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 3 | -3 | ([HCl])^(-3) Al(OH)_3 | 1 | -1 | ([Al(OH)3])^(-1) H_2O | 3 | 3 | ([H2O])^3 AlCl_3 | 1 | 1 | [AlCl3] 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])^(-3) ([Al(OH)3])^(-1) ([H2O])^3 [AlCl3] = (([H2O])^3 [AlCl3])/(([HCl])^3 [Al(OH)3])

Construct the rate of reaction expression for: HCl + Al(OH)_3 ⟶ H_2O + AlCl_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 HCl + Al(OH)_3 ⟶ 3 H_2O + AlCl_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 | 3 | -3 Al(OH)_3 | 1 | -1 H_2O | 3 | 3 AlCl_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 HCl | 3 | -3 | -1/3 (Δ[HCl])/(Δt) Al(OH)_3 | 1 | -1 | -(Δ[Al(OH)3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) AlCl_3 | 1 | 1 | (Δ[AlCl3])/(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[HCl])/(Δt) = -(Δ[Al(OH)3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[AlCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | aluminum hydroxide | water | aluminum chloride formula | HCl | Al(OH)_3 | H_2O | AlCl_3 Hill formula | ClH | AlH_3O_3 | H_2O | AlCl_3 name | hydrogen chloride | aluminum hydroxide | water | aluminum chloride IUPAC name | hydrogen chloride | aluminum hydroxide | water | trichloroalumane