Input interpretation
H_2O water + AuCl_3 gold(III) chloride + Au_2S_3 gold(III) sulfide ⟶ H_2SO_4 sulfuric acid + HCl hydrogen chloride + Au gold
Balanced equation
Balance the chemical equation algebraically: H_2O + AuCl_3 + Au_2S_3 ⟶ H_2SO_4 + HCl + Au Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AuCl_3 + c_3 Au_2S_3 ⟶ c_4 H_2SO_4 + c_5 HCl + c_6 Au Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Au, Cl and S: H: | 2 c_1 = 2 c_4 + c_5 O: | c_1 = 4 c_4 Au: | c_2 + 2 c_3 = c_6 Cl: | 3 c_2 = c_5 S: | 3 c_3 = c_4 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 = 12 c_2 = 6 c_3 = 1 c_4 = 3 c_5 = 18 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2O + 6 AuCl_3 + Au_2S_3 ⟶ 3 H_2SO_4 + 18 HCl + 8 Au
Structures
+ + ⟶ + +
Names
water + gold(III) chloride + gold(III) sulfide ⟶ sulfuric acid + hydrogen chloride + gold
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2O + AuCl_3 + Au_2S_3 ⟶ H_2SO_4 + HCl + 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: 12 H_2O + 6 AuCl_3 + Au_2S_3 ⟶ 3 H_2SO_4 + 18 HCl + 8 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 | 12 | -12 AuCl_3 | 6 | -6 Au_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 HCl | 18 | 18 Au | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 12 | -12 | ([H2O])^(-12) AuCl_3 | 6 | -6 | ([AuCl3])^(-6) Au_2S_3 | 1 | -1 | ([Au2S3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 HCl | 18 | 18 | ([HCl])^18 Au | 8 | 8 | ([Au])^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 = ([H2O])^(-12) ([AuCl3])^(-6) ([Au2S3])^(-1) ([H2SO4])^3 ([HCl])^18 ([Au])^8 = (([H2SO4])^3 ([HCl])^18 ([Au])^8)/(([H2O])^12 ([AuCl3])^6 [Au2S3])](../image_source/000bc229bbf8cc36384383554f282c35.png)
Construct the equilibrium constant, K, expression for: H_2O + AuCl_3 + Au_2S_3 ⟶ H_2SO_4 + HCl + 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: 12 H_2O + 6 AuCl_3 + Au_2S_3 ⟶ 3 H_2SO_4 + 18 HCl + 8 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 | 12 | -12 AuCl_3 | 6 | -6 Au_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 HCl | 18 | 18 Au | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 12 | -12 | ([H2O])^(-12) AuCl_3 | 6 | -6 | ([AuCl3])^(-6) Au_2S_3 | 1 | -1 | ([Au2S3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 HCl | 18 | 18 | ([HCl])^18 Au | 8 | 8 | ([Au])^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 = ([H2O])^(-12) ([AuCl3])^(-6) ([Au2S3])^(-1) ([H2SO4])^3 ([HCl])^18 ([Au])^8 = (([H2SO4])^3 ([HCl])^18 ([Au])^8)/(([H2O])^12 ([AuCl3])^6 [Au2S3])
Rate of reaction
![Construct the rate of reaction expression for: H_2O + AuCl_3 + Au_2S_3 ⟶ H_2SO_4 + HCl + 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: 12 H_2O + 6 AuCl_3 + Au_2S_3 ⟶ 3 H_2SO_4 + 18 HCl + 8 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 | 12 | -12 AuCl_3 | 6 | -6 Au_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 HCl | 18 | 18 Au | 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 H_2O | 12 | -12 | -1/12 (Δ[H2O])/(Δt) AuCl_3 | 6 | -6 | -1/6 (Δ[AuCl3])/(Δt) Au_2S_3 | 1 | -1 | -(Δ[Au2S3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) HCl | 18 | 18 | 1/18 (Δ[HCl])/(Δt) Au | 8 | 8 | 1/8 (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 = -1/12 (Δ[H2O])/(Δt) = -1/6 (Δ[AuCl3])/(Δt) = -(Δ[Au2S3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/18 (Δ[HCl])/(Δt) = 1/8 (Δ[Au])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/1827aee6edff6338416c5e851a7e4c34.png)
Construct the rate of reaction expression for: H_2O + AuCl_3 + Au_2S_3 ⟶ H_2SO_4 + HCl + 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: 12 H_2O + 6 AuCl_3 + Au_2S_3 ⟶ 3 H_2SO_4 + 18 HCl + 8 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 | 12 | -12 AuCl_3 | 6 | -6 Au_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 HCl | 18 | 18 Au | 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 H_2O | 12 | -12 | -1/12 (Δ[H2O])/(Δt) AuCl_3 | 6 | -6 | -1/6 (Δ[AuCl3])/(Δt) Au_2S_3 | 1 | -1 | -(Δ[Au2S3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) HCl | 18 | 18 | 1/18 (Δ[HCl])/(Δt) Au | 8 | 8 | 1/8 (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 = -1/12 (Δ[H2O])/(Δt) = -1/6 (Δ[AuCl3])/(Δt) = -(Δ[Au2S3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/18 (Δ[HCl])/(Δt) = 1/8 (Δ[Au])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| water | gold(III) chloride | gold(III) sulfide | sulfuric acid | hydrogen chloride | gold formula | H_2O | AuCl_3 | Au_2S_3 | H_2SO_4 | HCl | Au Hill formula | H_2O | AuCl_3 | Au_2S_3 | H_2O_4S | ClH | Au name | water | gold(III) chloride | gold(III) sulfide | sulfuric acid | hydrogen chloride | gold IUPAC name | water | trichlorogold | gold(+3) cation trisulfide | sulfuric acid | hydrogen chloride | gold