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KOH + H2O2 + AuCl3 = H2O + O2 + KCl + Au

Input interpretation

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

Balanced equation

Balance the chemical equation algebraically: KOH + H_2O_2 + AuCl_3 ⟶ H_2O + O_2 + KCl + Au Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 H_2O_2 + c_3 AuCl_3 ⟶ 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, K, O, Au and Cl: H: | c_1 + 2 c_2 = 2 c_4 K: | c_1 = c_6 O: | c_1 + 2 c_2 = c_4 + 2 c_5 Au: | c_3 = c_7 Cl: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = c_1/3 c_4 = c_1/2 + 1 c_5 = c_1/4 + 1/2 c_6 = c_1 c_7 = c_1/3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 6 and solve for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 2 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: | | 6 KOH + H_2O_2 + 2 AuCl_3 ⟶ 4 H_2O + 2 O_2 + 6 KCl + 2 Au
Balance the chemical equation algebraically: KOH + H_2O_2 + AuCl_3 ⟶ H_2O + O_2 + KCl + Au Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 H_2O_2 + c_3 AuCl_3 ⟶ 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, K, O, Au and Cl: H: | c_1 + 2 c_2 = 2 c_4 K: | c_1 = c_6 O: | c_1 + 2 c_2 = c_4 + 2 c_5 Au: | c_3 = c_7 Cl: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = c_1/3 c_4 = c_1/2 + 1 c_5 = c_1/4 + 1/2 c_6 = c_1 c_7 = c_1/3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 6 and solve for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 2 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: | | 6 KOH + H_2O_2 + 2 AuCl_3 ⟶ 4 H_2O + 2 O_2 + 6 KCl + 2 Au

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

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

Equilibrium constant

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

Rate of reaction

Construct the rate of reaction expression for: KOH + H_2O_2 + AuCl_3 ⟶ 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: 6 KOH + H_2O_2 + 2 AuCl_3 ⟶ 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 KOH | 6 | -6 H_2O_2 | 1 | -1 AuCl_3 | 2 | -2 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 KOH | 6 | -6 | -1/6 (Δ[KOH])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(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 = -1/6 (Δ[KOH])/(Δt) = -(Δ[H2O2])/(Δt) = -1/2 (Δ[AuCl3])/(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)
Construct the rate of reaction expression for: KOH + H_2O_2 + AuCl_3 ⟶ 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: 6 KOH + H_2O_2 + 2 AuCl_3 ⟶ 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 KOH | 6 | -6 H_2O_2 | 1 | -1 AuCl_3 | 2 | -2 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 KOH | 6 | -6 | -1/6 (Δ[KOH])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(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 = -1/6 (Δ[KOH])/(Δt) = -(Δ[H2O2])/(Δt) = -1/2 (Δ[AuCl3])/(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)

Chemical names and formulas

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

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