H2O + SnCl2 + H(AuCl4) = HCl + Au + SnO2

H_2O water + SnCl_2 stannous chloride + HAuCl_4·xH_2O gold(III) chloride hydrate ⟶ HCl hydrogen chloride + Au gold + SnO_2 stannic oxide

Balance the chemical equation algebraically: H_2O + SnCl_2 + HAuCl_4·xH_2O ⟶ HCl + Au + SnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SnCl_2 + c_3 HAuCl_4·xH_2O ⟶ c_4 HCl + c_5 Au + c_6 SnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, Sn and Au: H: | 2 c_1 + c_3 = c_4 O: | c_1 = 2 c_6 Cl: | 2 c_2 + 4 c_3 = c_4 Sn: | c_2 = c_6 Au: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3/2 c_3 = 1 c_4 = 7 c_5 = 1 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 3 c_3 = 2 c_4 = 14 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 3 SnCl_2 + 2 HAuCl_4·xH_2O ⟶ 14 HCl + 2 Au + 3 SnO_2

+ + ⟶ + +

water + stannous chloride + gold(III) chloride hydrate ⟶ hydrogen chloride + gold + stannic oxide

Construct the equilibrium constant, K, expression for: H_2O + SnCl_2 + HAuCl_4·xH_2O ⟶ HCl + Au + SnO_2 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 + 3 SnCl_2 + 2 HAuCl_4·xH_2O ⟶ 14 HCl + 2 Au + 3 SnO_2 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 SnCl_2 | 3 | -3 HAuCl_4·xH_2O | 2 | -2 HCl | 14 | 14 Au | 2 | 2 SnO_2 | 3 | 3 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) SnCl_2 | 3 | -3 | ([SnCl2])^(-3) HAuCl_4·xH_2O | 2 | -2 | ([HAuCl4·xH2O])^(-2) HCl | 14 | 14 | ([HCl])^14 Au | 2 | 2 | ([Au])^2 SnO_2 | 3 | 3 | ([SnO2])^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 = ([H2O])^(-6) ([SnCl2])^(-3) ([HAuCl4·xH2O])^(-2) ([HCl])^14 ([Au])^2 ([SnO2])^3 = (([HCl])^14 ([Au])^2 ([SnO2])^3)/(([H2O])^6 ([SnCl2])^3 ([HAuCl4·xH2O])^2)

Construct the rate of reaction expression for: H_2O + SnCl_2 + HAuCl_4·xH_2O ⟶ HCl + Au + SnO_2 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 + 3 SnCl_2 + 2 HAuCl_4·xH_2O ⟶ 14 HCl + 2 Au + 3 SnO_2 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 SnCl_2 | 3 | -3 HAuCl_4·xH_2O | 2 | -2 HCl | 14 | 14 Au | 2 | 2 SnO_2 | 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 H_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) SnCl_2 | 3 | -3 | -1/3 (Δ[SnCl2])/(Δt) HAuCl_4·xH_2O | 2 | -2 | -1/2 (Δ[HAuCl4·xH2O])/(Δt) HCl | 14 | 14 | 1/14 (Δ[HCl])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(Δt) SnO_2 | 3 | 3 | 1/3 (Δ[SnO2])/(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) = -1/3 (Δ[SnCl2])/(Δt) = -1/2 (Δ[HAuCl4·xH2O])/(Δt) = 1/14 (Δ[HCl])/(Δt) = 1/2 (Δ[Au])/(Δt) = 1/3 (Δ[SnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | stannous chloride | gold(III) chloride hydrate | hydrogen chloride | gold | stannic oxide formula | H_2O | SnCl_2 | HAuCl_4·xH_2O | HCl | Au | SnO_2 Hill formula | H_2O | Cl_2Sn | AuCl_4H | ClH | Au | O_2Sn name | water | stannous chloride | gold(III) chloride hydrate | hydrogen chloride | gold | stannic oxide IUPAC name | water | dichlorotin | hydron; tetrachlorogold | hydrogen chloride | gold |