H2O + AlCl3 + Na2S = NaCl + H2S + Al(OH)3

H_2O water + AlCl_3 aluminum chloride + Na_2S sodium sulfide ⟶ NaCl sodium chloride + H_2S hydrogen sulfide + Al(OH)_3 aluminum hydroxide

Balance the chemical equation algebraically: H_2O + AlCl_3 + Na_2S ⟶ NaCl + H_2S + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AlCl_3 + c_3 Na_2S ⟶ c_4 NaCl + c_5 H_2S + c_6 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al, Cl, Na and S: H: | 2 c_1 = 2 c_5 + 3 c_6 O: | c_1 = 3 c_6 Al: | c_2 = c_6 Cl: | 3 c_2 = c_4 Na: | 2 c_3 = c_4 S: | c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3/2 c_4 = 3 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 6 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 2 AlCl_3 + 3 Na_2S ⟶ 6 NaCl + 3 H_2S + 2 Al(OH)_3

+ + ⟶ + +

water + aluminum chloride + sodium sulfide ⟶ sodium chloride + hydrogen sulfide + aluminum hydroxide

Construct the equilibrium constant, K, expression for: H_2O + AlCl_3 + Na_2S ⟶ NaCl + H_2S + Al(OH)_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: 6 H_2O + 2 AlCl_3 + 3 Na_2S ⟶ 6 NaCl + 3 H_2S + 2 Al(OH)_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 | 6 | -6 AlCl_3 | 2 | -2 Na_2S | 3 | -3 NaCl | 6 | 6 H_2S | 3 | 3 Al(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) AlCl_3 | 2 | -2 | ([AlCl3])^(-2) Na_2S | 3 | -3 | ([Na2S])^(-3) NaCl | 6 | 6 | ([NaCl])^6 H_2S | 3 | 3 | ([H2S])^3 Al(OH)_3 | 2 | 2 | ([Al(OH)3])^2 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])^(-6) ([AlCl3])^(-2) ([Na2S])^(-3) ([NaCl])^6 ([H2S])^3 ([Al(OH)3])^2 = (([NaCl])^6 ([H2S])^3 ([Al(OH)3])^2)/(([H2O])^6 ([AlCl3])^2 ([Na2S])^3)

Construct the rate of reaction expression for: H_2O + AlCl_3 + Na_2S ⟶ NaCl + H_2S + Al(OH)_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: 6 H_2O + 2 AlCl_3 + 3 Na_2S ⟶ 6 NaCl + 3 H_2S + 2 Al(OH)_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 | 6 | -6 AlCl_3 | 2 | -2 Na_2S | 3 | -3 NaCl | 6 | 6 H_2S | 3 | 3 Al(OH)_3 | 2 | 2 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 | 6 | -6 | -1/6 (Δ[H2O])/(Δt) AlCl_3 | 2 | -2 | -1/2 (Δ[AlCl3])/(Δt) Na_2S | 3 | -3 | -1/3 (Δ[Na2S])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(Δt) H_2S | 3 | 3 | 1/3 (Δ[H2S])/(Δt) Al(OH)_3 | 2 | 2 | 1/2 (Δ[Al(OH)3])/(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[H2O])/(Δt) = -1/2 (Δ[AlCl3])/(Δt) = -1/3 (Δ[Na2S])/(Δt) = 1/6 (Δ[NaCl])/(Δt) = 1/3 (Δ[H2S])/(Δt) = 1/2 (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | aluminum chloride | sodium sulfide | sodium chloride | hydrogen sulfide | aluminum hydroxide formula | H_2O | AlCl_3 | Na_2S | NaCl | H_2S | Al(OH)_3 Hill formula | H_2O | AlCl_3 | Na_2S_1 | ClNa | H_2S | AlH_3O_3 name | water | aluminum chloride | sodium sulfide | sodium chloride | hydrogen sulfide | aluminum hydroxide IUPAC name | water | trichloroalumane | | sodium chloride | hydrogen sulfide | aluminum hydroxide

| water | aluminum chloride | sodium sulfide | sodium chloride | hydrogen sulfide | aluminum hydroxide molar mass | 18.015 g/mol | 133.3 g/mol | 78.04 g/mol | 58.44 g/mol | 34.08 g/mol | 78.003 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | 190 °C | 1172 °C | 801 °C | -85 °C | boiling point | 99.9839 °C | | | 1413 °C | -60 °C | density | 1 g/cm^3 | | 1.856 g/cm^3 | 2.16 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | solubility in water | | | | soluble | | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | 1.239×10^-5 Pa s (at 25 °C) | odor | odorless | | | odorless | |