H2O2 + AuCl3 + K(OH) = H2O + O2 + KCl + Au

H_2O_2 hydrogen peroxide + AuCl_3 gold(III) chloride + KOH potassium hydroxide ⟶ H_2O water + O_2 oxygen + KCl potassium chloride + Au gold

Balance the chemical equation algebraically: H_2O_2 + AuCl_3 + KOH ⟶ H_2O + O_2 + KCl + Au Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 AuCl_3 + c_3 KOH ⟶ c_4 H_2O + c_5 O_2 + c_6 KCl + c_7 Au Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Au, Cl and K: H: | 2 c_1 + c_3 = 2 c_4 O: | 2 c_1 + c_3 = c_4 + 2 c_5 Au: | c_2 = c_7 Cl: | 3 c_2 = c_6 K: | c_3 = c_6 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_3 = 3 c_2 c_4 = (3 c_2)/2 + 1 c_5 = (3 c_2)/4 + 1/2 c_6 = 3 c_2 c_7 = c_2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 2 and solve for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 6 c_4 = 4 c_5 = 2 c_6 = 6 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O_2 + 2 AuCl_3 + 6 KOH ⟶ 4 H_2O + 2 O_2 + 6 KCl + 2 Au

+ + ⟶ + + +

hydrogen peroxide + gold(III) chloride + potassium hydroxide ⟶ water + oxygen + potassium chloride + gold

Construct the equilibrium constant, K, expression for: H_2O_2 + AuCl_3 + KOH ⟶ H_2O + O_2 + KCl + Au 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: H_2O_2 + 2 AuCl_3 + 6 KOH ⟶ 4 H_2O + 2 O_2 + 6 KCl + 2 Au 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_2 | 1 | -1 AuCl_3 | 2 | -2 KOH | 6 | -6 H_2O | 4 | 4 O_2 | 2 | 2 KCl | 6 | 6 Au | 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_2 | 1 | -1 | ([H2O2])^(-1) AuCl_3 | 2 | -2 | ([AuCl3])^(-2) KOH | 6 | -6 | ([KOH])^(-6) H_2O | 4 | 4 | ([H2O])^4 O_2 | 2 | 2 | ([O2])^2 KCl | 6 | 6 | ([KCl])^6 Au | 2 | 2 | ([Au])^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 = ([H2O2])^(-1) ([AuCl3])^(-2) ([KOH])^(-6) ([H2O])^4 ([O2])^2 ([KCl])^6 ([Au])^2 = (([H2O])^4 ([O2])^2 ([KCl])^6 ([Au])^2)/([H2O2] ([AuCl3])^2 ([KOH])^6)

Construct the rate of reaction expression for: H_2O_2 + AuCl_3 + KOH ⟶ H_2O + O_2 + KCl + Au 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: H_2O_2 + 2 AuCl_3 + 6 KOH ⟶ 4 H_2O + 2 O_2 + 6 KCl + 2 Au 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_2 | 1 | -1 AuCl_3 | 2 | -2 KOH | 6 | -6 H_2O | 4 | 4 O_2 | 2 | 2 KCl | 6 | 6 Au | 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_2 | 1 | -1 | -(Δ[H2O2])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(Δt) KOH | 6 | -6 | -1/6 (Δ[KOH])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) KCl | 6 | 6 | 1/6 (Δ[KCl])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(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[H2O2])/(Δt) = -1/2 (Δ[AuCl3])/(Δt) = -1/6 (Δ[KOH])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = 1/6 (Δ[KCl])/(Δt) = 1/2 (Δ[Au])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen peroxide | gold(III) chloride | potassium hydroxide | water | oxygen | potassium chloride | gold formula | H_2O_2 | AuCl_3 | KOH | H_2O | O_2 | KCl | Au Hill formula | H_2O_2 | AuCl_3 | HKO | H_2O | O_2 | ClK | Au name | hydrogen peroxide | gold(III) chloride | potassium hydroxide | water | oxygen | potassium chloride | gold IUPAC name | hydrogen peroxide | trichlorogold | potassium hydroxide | water | molecular oxygen | potassium chloride | gold