H2O + Cl2 + As2S3 = HCl + S + H3AsO4

H_2O (water) + Cl_2 (chlorine) + 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 + Cl_2 + As_2S_3 ⟶ HCl + S + H_3AsO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + 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_4 + 3 c_6 O: | c_1 = 4 c_6 Cl: | 2 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 = 8 c_2 = 5 c_3 = 1 c_4 = 10 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2O + 5 Cl_2 + As_2S_3 ⟶ 10 HCl + 3 S + 2 H_3AsO_4

+ + ⟶ + +

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

Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + 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: 8 H_2O + 5 Cl_2 + As_2S_3 ⟶ 10 HCl + 3 S + 2 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 | 8 | -8 Cl_2 | 5 | -5 As_2S_3 | 1 | -1 HCl | 10 | 10 S | 3 | 3 H_3AsO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 8 | -8 | ([H2O])^(-8) Cl_2 | 5 | -5 | ([Cl2])^(-5) As_2S_3 | 1 | -1 | ([As2S3])^(-1) HCl | 10 | 10 | ([HCl])^10 S | 3 | 3 | ([S])^3 H_3AsO_4 | 2 | 2 | ([H3AsO4])^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 = ([H2O])^(-8) ([Cl2])^(-5) ([As2S3])^(-1) ([HCl])^10 ([S])^3 ([H3AsO4])^2 = (([HCl])^10 ([S])^3 ([H3AsO4])^2)/(([H2O])^8 ([Cl2])^5 [As2S3])

Construct the rate of reaction expression for: H_2O + Cl_2 + 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: 8 H_2O + 5 Cl_2 + As_2S_3 ⟶ 10 HCl + 3 S + 2 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 | 8 | -8 Cl_2 | 5 | -5 As_2S_3 | 1 | -1 HCl | 10 | 10 S | 3 | 3 H_3AsO_4 | 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 H_2O | 8 | -8 | -1/8 (Δ[H2O])/(Δt) Cl_2 | 5 | -5 | -1/5 (Δ[Cl2])/(Δt) As_2S_3 | 1 | -1 | -(Δ[As2S3])/(Δt) HCl | 10 | 10 | 1/10 (Δ[HCl])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) H_3AsO_4 | 2 | 2 | 1/2 (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 = -1/8 (Δ[H2O])/(Δt) = -1/5 (Δ[Cl2])/(Δt) = -(Δ[As2S3])/(Δt) = 1/10 (Δ[HCl])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/2 (Δ[H3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | chlorine | arsenic(III) sulfide | hydrogen chloride | mixed sulfur | arsenic acid, solid formula | H_2O | Cl_2 | As_2S_3 | HCl | S | H_3AsO_4 Hill formula | H_2O | Cl_2 | As_2S_3 | ClH | S | AsH_3O_4 name | water | chlorine | arsenic(III) sulfide | hydrogen chloride | mixed sulfur | arsenic acid, solid IUPAC name | water | molecular chlorine | | hydrogen chloride | sulfur | arsoric acid

| water | chlorine | arsenic(III) sulfide | hydrogen chloride | mixed sulfur | arsenic acid, solid molar mass | 18.015 g/mol | 70.9 g/mol | 246 g/mol | 36.46 g/mol | 32.06 g/mol | 141.94 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | -101 °C | 300 °C | -114.17 °C | 112.8 °C | 35.5 °C boiling point | 99.9839 °C | -34 °C | | -85 °C | 444.7 °C | 160 °C density | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 3.43 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | 2.07 g/cm^3 | 2.2 g/cm^3 solubility in water | | | | miscible | | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | | odor | odorless | | | | |