AlCl3 + NH4OH = Al(OH)3 + NH4Cl

AlCl_3 aluminum chloride + NH_4OH ammonium hydroxide ⟶ Al(OH)_3 aluminum hydroxide + NH_4Cl ammonium chloride

Balance the chemical equation algebraically: AlCl_3 + NH_4OH ⟶ Al(OH)_3 + NH_4Cl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AlCl_3 + c_2 NH_4OH ⟶ c_3 Al(OH)_3 + c_4 NH_4Cl Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Cl, H, N and O: Al: | c_1 = c_3 Cl: | 3 c_1 = c_4 H: | 5 c_2 = 3 c_3 + 4 c_4 N: | c_2 = c_4 O: | c_2 = 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | AlCl_3 + 3 NH_4OH ⟶ Al(OH)_3 + 3 NH_4Cl

+ ⟶ +

aluminum chloride + ammonium hydroxide ⟶ aluminum hydroxide + ammonium chloride

Construct the equilibrium constant, K, expression for: AlCl_3 + NH_4OH ⟶ Al(OH)_3 + NH_4Cl 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: AlCl_3 + 3 NH_4OH ⟶ Al(OH)_3 + 3 NH_4Cl 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 AlCl_3 | 1 | -1 NH_4OH | 3 | -3 Al(OH)_3 | 1 | 1 NH_4Cl | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AlCl_3 | 1 | -1 | ([AlCl3])^(-1) NH_4OH | 3 | -3 | ([NH4OH])^(-3) Al(OH)_3 | 1 | 1 | [Al(OH)3] NH_4Cl | 3 | 3 | ([NH4Cl])^3 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 = ([AlCl3])^(-1) ([NH4OH])^(-3) [Al(OH)3] ([NH4Cl])^3 = ([Al(OH)3] ([NH4Cl])^3)/([AlCl3] ([NH4OH])^3)

Construct the rate of reaction expression for: AlCl_3 + NH_4OH ⟶ Al(OH)_3 + NH_4Cl 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: AlCl_3 + 3 NH_4OH ⟶ Al(OH)_3 + 3 NH_4Cl 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 AlCl_3 | 1 | -1 NH_4OH | 3 | -3 Al(OH)_3 | 1 | 1 NH_4Cl | 3 | 3 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 AlCl_3 | 1 | -1 | -(Δ[AlCl3])/(Δt) NH_4OH | 3 | -3 | -1/3 (Δ[NH4OH])/(Δt) Al(OH)_3 | 1 | 1 | (Δ[Al(OH)3])/(Δt) NH_4Cl | 3 | 3 | 1/3 (Δ[NH4Cl])/(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 = -(Δ[AlCl3])/(Δt) = -1/3 (Δ[NH4OH])/(Δt) = (Δ[Al(OH)3])/(Δt) = 1/3 (Δ[NH4Cl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum chloride | ammonium hydroxide | aluminum hydroxide | ammonium chloride formula | AlCl_3 | NH_4OH | Al(OH)_3 | NH_4Cl Hill formula | AlCl_3 | H_5NO | AlH_3O_3 | ClH_4N name | aluminum chloride | ammonium hydroxide | aluminum hydroxide | ammonium chloride IUPAC name | trichloroalumane | ammonium hydroxide | aluminum hydroxide | ammonium chloride

| aluminum chloride | ammonium hydroxide | aluminum hydroxide | ammonium chloride molar mass | 133.3 g/mol | 35.046 g/mol | 78.003 g/mol | 53.49 g/mol phase | solid (at STP) | aqueous (at STP) | | solid (at STP) melting point | 190 °C | -57.5 °C | | 340 °C boiling point | | 36 °C | | density | | 0.9 g/cm^3 | | 1.5256 g/cm^3 solubility in water | | very soluble | | soluble