H2O + HClO4 + As2S3 = HCl + S + H3AsO4

H_2O water + HClO_4 perchloric acid + As_2S_3 arsenic(III) sulfide ⟶ HCl hydrogen chloride + S mixed sulfur + H_3AsO_4 arsenic acid, solid

Balance the chemical equation algebraically: H_2O + HClO_4 + As_2S_3 ⟶ HCl + S + H_3AsO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HClO_4 + c_3 As_2S_3 ⟶ c_4 HCl + c_5 S + c_6 H_3AsO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, As and S: H: | 2 c_1 + c_2 = c_4 + 3 c_6 O: | c_1 + 4 c_2 = 4 c_6 Cl: | c_2 = c_4 As: | 2 c_3 = c_6 S: | 3 c_3 = c_5 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 = 5/4 c_3 = 1 c_4 = 5/4 c_5 = 3 c_6 = 2 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 5 c_3 = 4 c_4 = 5 c_5 = 12 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2O + 5 HClO_4 + 4 As_2S_3 ⟶ 5 HCl + 12 S + 8 H_3AsO_4

+ + ⟶ + +

water + perchloric acid + arsenic(III) sulfide ⟶ hydrogen chloride + mixed sulfur + arsenic acid, solid

Construct the equilibrium constant, K, expression for: H_2O + HClO_4 + As_2S_3 ⟶ HCl + S + H_3AsO_4 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 + 5 HClO_4 + 4 As_2S_3 ⟶ 5 HCl + 12 S + 8 H_3AsO_4 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 HClO_4 | 5 | -5 As_2S_3 | 4 | -4 HCl | 5 | 5 S | 12 | 12 H_3AsO_4 | 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) HClO_4 | 5 | -5 | ([HClO4])^(-5) As_2S_3 | 4 | -4 | ([As2S3])^(-4) HCl | 5 | 5 | ([HCl])^5 S | 12 | 12 | ([S])^12 H_3AsO_4 | 8 | 8 | ([H3AsO4])^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) ([HClO4])^(-5) ([As2S3])^(-4) ([HCl])^5 ([S])^12 ([H3AsO4])^8 = (([HCl])^5 ([S])^12 ([H3AsO4])^8)/(([H2O])^12 ([HClO4])^5 ([As2S3])^4)

Construct the rate of reaction expression for: H_2O + HClO_4 + As_2S_3 ⟶ HCl + S + H_3AsO_4 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 + 5 HClO_4 + 4 As_2S_3 ⟶ 5 HCl + 12 S + 8 H_3AsO_4 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 HClO_4 | 5 | -5 As_2S_3 | 4 | -4 HCl | 5 | 5 S | 12 | 12 H_3AsO_4 | 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) HClO_4 | 5 | -5 | -1/5 (Δ[HClO4])/(Δt) As_2S_3 | 4 | -4 | -1/4 (Δ[As2S3])/(Δt) HCl | 5 | 5 | 1/5 (Δ[HCl])/(Δt) S | 12 | 12 | 1/12 (Δ[S])/(Δt) H_3AsO_4 | 8 | 8 | 1/8 (Δ[H3AsO4])/(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) = -1/5 (Δ[HClO4])/(Δt) = -1/4 (Δ[As2S3])/(Δt) = 1/5 (Δ[HCl])/(Δt) = 1/12 (Δ[S])/(Δt) = 1/8 (Δ[H3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | perchloric acid | arsenic(III) sulfide | hydrogen chloride | mixed sulfur | arsenic acid, solid formula | H_2O | HClO_4 | As_2S_3 | HCl | S | H_3AsO_4 Hill formula | H_2O | ClHO_4 | As_2S_3 | ClH | S | AsH_3O_4 name | water | perchloric acid | arsenic(III) sulfide | hydrogen chloride | mixed sulfur | arsenic acid, solid IUPAC name | water | perchloric acid | | hydrogen chloride | sulfur | arsoric acid