Input interpretation
NaOH sodium hydroxide + H_2O_2 hydrogen peroxide + HAuCl_4·xH_2O gold(III) chloride hydrate ⟶ H_2O water + O_2 oxygen + Au gold + NaCl sodium chloride
Balanced equation
Balance the chemical equation algebraically: NaOH + H_2O_2 + HAuCl_4·xH_2O ⟶ H_2O + O_2 + Au + NaCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 H_2O_2 + c_3 HAuCl_4·xH_2O ⟶ c_4 H_2O + c_5 O_2 + c_6 Au + c_7 NaCl Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Au and Cl: H: | c_1 + 2 c_2 + c_3 = 2 c_4 Na: | c_1 = c_7 O: | c_1 + 2 c_2 = c_4 + 2 c_5 Au: | c_3 = c_6 Cl: | 4 c_3 = c_7 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_1/4 c_4 = (5 c_1)/8 + 1 c_5 = (3 c_1)/16 + 1/2 c_6 = c_1/4 c_7 = c_1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 8 and solve for the remaining coefficients: c_1 = 8 c_2 = 1 c_3 = 2 c_4 = 6 c_5 = 2 c_6 = 2 c_7 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 NaOH + H_2O_2 + 2 HAuCl_4·xH_2O ⟶ 6 H_2O + 2 O_2 + 2 Au + 8 NaCl
Structures
+ + ⟶ + + +
Names
sodium hydroxide + hydrogen peroxide + gold(III) chloride hydrate ⟶ water + oxygen + gold + sodium chloride
Equilibrium constant
![Construct the equilibrium constant, K, expression for: NaOH + H_2O_2 + HAuCl_4·xH_2O ⟶ H_2O + O_2 + Au + NaCl 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: 8 NaOH + H_2O_2 + 2 HAuCl_4·xH_2O ⟶ 6 H_2O + 2 O_2 + 2 Au + 8 NaCl 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 NaOH | 8 | -8 H_2O_2 | 1 | -1 HAuCl_4·xH_2O | 2 | -2 H_2O | 6 | 6 O_2 | 2 | 2 Au | 2 | 2 NaCl | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 8 | -8 | ([NaOH])^(-8) H_2O_2 | 1 | -1 | ([H2O2])^(-1) HAuCl_4·xH_2O | 2 | -2 | ([HAuCl4·xH2O])^(-2) H_2O | 6 | 6 | ([H2O])^6 O_2 | 2 | 2 | ([O2])^2 Au | 2 | 2 | ([Au])^2 NaCl | 8 | 8 | ([NaCl])^8 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 = ([NaOH])^(-8) ([H2O2])^(-1) ([HAuCl4·xH2O])^(-2) ([H2O])^6 ([O2])^2 ([Au])^2 ([NaCl])^8 = (([H2O])^6 ([O2])^2 ([Au])^2 ([NaCl])^8)/(([NaOH])^8 [H2O2] ([HAuCl4·xH2O])^2)](../image_source/53334b58a5829f662750255ad44c5fa4.png)
Construct the equilibrium constant, K, expression for: NaOH + H_2O_2 + HAuCl_4·xH_2O ⟶ H_2O + O_2 + Au + NaCl 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: 8 NaOH + H_2O_2 + 2 HAuCl_4·xH_2O ⟶ 6 H_2O + 2 O_2 + 2 Au + 8 NaCl 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 NaOH | 8 | -8 H_2O_2 | 1 | -1 HAuCl_4·xH_2O | 2 | -2 H_2O | 6 | 6 O_2 | 2 | 2 Au | 2 | 2 NaCl | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 8 | -8 | ([NaOH])^(-8) H_2O_2 | 1 | -1 | ([H2O2])^(-1) HAuCl_4·xH_2O | 2 | -2 | ([HAuCl4·xH2O])^(-2) H_2O | 6 | 6 | ([H2O])^6 O_2 | 2 | 2 | ([O2])^2 Au | 2 | 2 | ([Au])^2 NaCl | 8 | 8 | ([NaCl])^8 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 = ([NaOH])^(-8) ([H2O2])^(-1) ([HAuCl4·xH2O])^(-2) ([H2O])^6 ([O2])^2 ([Au])^2 ([NaCl])^8 = (([H2O])^6 ([O2])^2 ([Au])^2 ([NaCl])^8)/(([NaOH])^8 [H2O2] ([HAuCl4·xH2O])^2)
Rate of reaction
![Construct the rate of reaction expression for: NaOH + H_2O_2 + HAuCl_4·xH_2O ⟶ H_2O + O_2 + Au + NaCl 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: 8 NaOH + H_2O_2 + 2 HAuCl_4·xH_2O ⟶ 6 H_2O + 2 O_2 + 2 Au + 8 NaCl 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 NaOH | 8 | -8 H_2O_2 | 1 | -1 HAuCl_4·xH_2O | 2 | -2 H_2O | 6 | 6 O_2 | 2 | 2 Au | 2 | 2 NaCl | 8 | 8 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 NaOH | 8 | -8 | -1/8 (Δ[NaOH])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) HAuCl_4·xH_2O | 2 | -2 | -1/2 (Δ[HAuCl4·xH2O])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(Δt) NaCl | 8 | 8 | 1/8 (Δ[NaCl])/(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 = -1/8 (Δ[NaOH])/(Δt) = -(Δ[H2O2])/(Δt) = -1/2 (Δ[HAuCl4·xH2O])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = 1/2 (Δ[Au])/(Δt) = 1/8 (Δ[NaCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/b0772018a2a8d7eca7076ef573e4fae9.png)
Construct the rate of reaction expression for: NaOH + H_2O_2 + HAuCl_4·xH_2O ⟶ H_2O + O_2 + Au + NaCl 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: 8 NaOH + H_2O_2 + 2 HAuCl_4·xH_2O ⟶ 6 H_2O + 2 O_2 + 2 Au + 8 NaCl 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 NaOH | 8 | -8 H_2O_2 | 1 | -1 HAuCl_4·xH_2O | 2 | -2 H_2O | 6 | 6 O_2 | 2 | 2 Au | 2 | 2 NaCl | 8 | 8 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 NaOH | 8 | -8 | -1/8 (Δ[NaOH])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) HAuCl_4·xH_2O | 2 | -2 | -1/2 (Δ[HAuCl4·xH2O])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(Δt) NaCl | 8 | 8 | 1/8 (Δ[NaCl])/(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 = -1/8 (Δ[NaOH])/(Δt) = -(Δ[H2O2])/(Δt) = -1/2 (Δ[HAuCl4·xH2O])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = 1/2 (Δ[Au])/(Δt) = 1/8 (Δ[NaCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sodium hydroxide | hydrogen peroxide | gold(III) chloride hydrate | water | oxygen | gold | sodium chloride formula | NaOH | H_2O_2 | HAuCl_4·xH_2O | H_2O | O_2 | Au | NaCl Hill formula | HNaO | H_2O_2 | AuCl_4H | H_2O | O_2 | Au | ClNa name | sodium hydroxide | hydrogen peroxide | gold(III) chloride hydrate | water | oxygen | gold | sodium chloride IUPAC name | sodium hydroxide | hydrogen peroxide | hydron; tetrachlorogold | water | molecular oxygen | gold | sodium chloride