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H2O + AuCl3 + AsH3 = HCl + Au + H3AsO3

Input interpretation

H_2O water + AuCl_3 gold(III) chloride + AsH_3 arsine ⟶ HCl hydrogen chloride + Au gold + As(OH)_3 arsenious acid
H_2O water + AuCl_3 gold(III) chloride + AsH_3 arsine ⟶ HCl hydrogen chloride + Au gold + As(OH)_3 arsenious acid

Balanced equation

Balance the chemical equation algebraically: H_2O + AuCl_3 + AsH_3 ⟶ HCl + Au + As(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AuCl_3 + c_3 AsH_3 ⟶ c_4 HCl + c_5 Au + c_6 As(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Au, Cl and As: H: | 2 c_1 + 3 c_3 = c_4 + 3 c_6 O: | c_1 = 3 c_6 Au: | c_2 = c_5 Cl: | 3 c_2 = c_4 As: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 6 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 AuCl_3 + AsH_3 ⟶ 6 HCl + 2 Au + As(OH)_3
Balance the chemical equation algebraically: H_2O + AuCl_3 + AsH_3 ⟶ HCl + Au + As(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AuCl_3 + c_3 AsH_3 ⟶ c_4 HCl + c_5 Au + c_6 As(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Au, Cl and As: H: | 2 c_1 + 3 c_3 = c_4 + 3 c_6 O: | c_1 = 3 c_6 Au: | c_2 = c_5 Cl: | 3 c_2 = c_4 As: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 6 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 AuCl_3 + AsH_3 ⟶ 6 HCl + 2 Au + As(OH)_3

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + gold(III) chloride + arsine ⟶ hydrogen chloride + gold + arsenious acid
water + gold(III) chloride + arsine ⟶ hydrogen chloride + gold + arsenious acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + AuCl_3 + AsH_3 ⟶ HCl + Au + As(OH)_3 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: 3 H_2O + 2 AuCl_3 + AsH_3 ⟶ 6 HCl + 2 Au + As(OH)_3 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 | 3 | -3 AuCl_3 | 2 | -2 AsH_3 | 1 | -1 HCl | 6 | 6 Au | 2 | 2 As(OH)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) AuCl_3 | 2 | -2 | ([AuCl3])^(-2) AsH_3 | 1 | -1 | ([AsH3])^(-1) HCl | 6 | 6 | ([HCl])^6 Au | 2 | 2 | ([Au])^2 As(OH)_3 | 1 | 1 | [As(OH)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])^(-3) ([AuCl3])^(-2) ([AsH3])^(-1) ([HCl])^6 ([Au])^2 [As(OH)3] = (([HCl])^6 ([Au])^2 [As(OH)3])/(([H2O])^3 ([AuCl3])^2 [AsH3])
Construct the equilibrium constant, K, expression for: H_2O + AuCl_3 + AsH_3 ⟶ HCl + Au + As(OH)_3 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: 3 H_2O + 2 AuCl_3 + AsH_3 ⟶ 6 HCl + 2 Au + As(OH)_3 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 | 3 | -3 AuCl_3 | 2 | -2 AsH_3 | 1 | -1 HCl | 6 | 6 Au | 2 | 2 As(OH)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) AuCl_3 | 2 | -2 | ([AuCl3])^(-2) AsH_3 | 1 | -1 | ([AsH3])^(-1) HCl | 6 | 6 | ([HCl])^6 Au | 2 | 2 | ([Au])^2 As(OH)_3 | 1 | 1 | [As(OH)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])^(-3) ([AuCl3])^(-2) ([AsH3])^(-1) ([HCl])^6 ([Au])^2 [As(OH)3] = (([HCl])^6 ([Au])^2 [As(OH)3])/(([H2O])^3 ([AuCl3])^2 [AsH3])

Rate of reaction

Construct the rate of reaction expression for: H_2O + AuCl_3 + AsH_3 ⟶ HCl + Au + As(OH)_3 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: 3 H_2O + 2 AuCl_3 + AsH_3 ⟶ 6 HCl + 2 Au + As(OH)_3 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 | 3 | -3 AuCl_3 | 2 | -2 AsH_3 | 1 | -1 HCl | 6 | 6 Au | 2 | 2 As(OH)_3 | 1 | 1 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(Δt) AsH_3 | 1 | -1 | -(Δ[AsH3])/(Δt) HCl | 6 | 6 | 1/6 (Δ[HCl])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(Δt) As(OH)_3 | 1 | 1 | (Δ[As(OH)3])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[AuCl3])/(Δt) = -(Δ[AsH3])/(Δt) = 1/6 (Δ[HCl])/(Δt) = 1/2 (Δ[Au])/(Δt) = (Δ[As(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + AuCl_3 + AsH_3 ⟶ HCl + Au + As(OH)_3 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: 3 H_2O + 2 AuCl_3 + AsH_3 ⟶ 6 HCl + 2 Au + As(OH)_3 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 | 3 | -3 AuCl_3 | 2 | -2 AsH_3 | 1 | -1 HCl | 6 | 6 Au | 2 | 2 As(OH)_3 | 1 | 1 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(Δt) AsH_3 | 1 | -1 | -(Δ[AsH3])/(Δt) HCl | 6 | 6 | 1/6 (Δ[HCl])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(Δt) As(OH)_3 | 1 | 1 | (Δ[As(OH)3])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[AuCl3])/(Δt) = -(Δ[AsH3])/(Δt) = 1/6 (Δ[HCl])/(Δt) = 1/2 (Δ[Au])/(Δt) = (Δ[As(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | gold(III) chloride | arsine | hydrogen chloride | gold | arsenious acid formula | H_2O | AuCl_3 | AsH_3 | HCl | Au | As(OH)_3 Hill formula | H_2O | AuCl_3 | AsH_3 | ClH | Au | AsH_3O_3 name | water | gold(III) chloride | arsine | hydrogen chloride | gold | arsenious acid IUPAC name | water | trichlorogold | arsane | hydrogen chloride | gold | arsorous acid
| water | gold(III) chloride | arsine | hydrogen chloride | gold | arsenious acid formula | H_2O | AuCl_3 | AsH_3 | HCl | Au | As(OH)_3 Hill formula | H_2O | AuCl_3 | AsH_3 | ClH | Au | AsH_3O_3 name | water | gold(III) chloride | arsine | hydrogen chloride | gold | arsenious acid IUPAC name | water | trichlorogold | arsane | hydrogen chloride | gold | arsorous acid

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