H2O + As2S3 + KClO4 = H2SO4 + KCl + H3AsO4

H_2O water + As_2S_3 arsenic(III) sulfide + KClO_4 potassium perchlorate ⟶ H_2SO_4 sulfuric acid + KCl potassium chloride + H_3AsO_4 arsenic acid, solid

Balance the chemical equation algebraically: H_2O + As_2S_3 + KClO_4 ⟶ H_2SO_4 + KCl + H_3AsO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 As_2S_3 + c_3 KClO_4 ⟶ c_4 H_2SO_4 + c_5 KCl + 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, As, S, Cl and K: H: | 2 c_1 = 2 c_4 + 3 c_6 O: | c_1 + 4 c_3 = 4 c_4 + 4 c_6 As: | 2 c_2 = c_6 S: | 3 c_2 = c_4 Cl: | c_3 = c_5 K: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 7/2 c_4 = 3 c_5 = 7/2 c_6 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 12 c_2 = 2 c_3 = 7 c_4 = 6 c_5 = 7 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2O + 2 As_2S_3 + 7 KClO_4 ⟶ 6 H_2SO_4 + 7 KCl + 4 H_3AsO_4

+ + ⟶ + +

water + arsenic(III) sulfide + potassium perchlorate ⟶ sulfuric acid + potassium chloride + arsenic acid, solid

Construct the equilibrium constant, K, expression for: H_2O + As_2S_3 + KClO_4 ⟶ H_2SO_4 + KCl + 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 + 2 As_2S_3 + 7 KClO_4 ⟶ 6 H_2SO_4 + 7 KCl + 4 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 As_2S_3 | 2 | -2 KClO_4 | 7 | -7 H_2SO_4 | 6 | 6 KCl | 7 | 7 H_3AsO_4 | 4 | 4 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) As_2S_3 | 2 | -2 | ([As2S3])^(-2) KClO_4 | 7 | -7 | ([KClO4])^(-7) H_2SO_4 | 6 | 6 | ([H2SO4])^6 KCl | 7 | 7 | ([KCl])^7 H_3AsO_4 | 4 | 4 | ([H3AsO4])^4 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) ([As2S3])^(-2) ([KClO4])^(-7) ([H2SO4])^6 ([KCl])^7 ([H3AsO4])^4 = (([H2SO4])^6 ([KCl])^7 ([H3AsO4])^4)/(([H2O])^12 ([As2S3])^2 ([KClO4])^7)

Construct the rate of reaction expression for: H_2O + As_2S_3 + KClO_4 ⟶ H_2SO_4 + KCl + 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 + 2 As_2S_3 + 7 KClO_4 ⟶ 6 H_2SO_4 + 7 KCl + 4 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 As_2S_3 | 2 | -2 KClO_4 | 7 | -7 H_2SO_4 | 6 | 6 KCl | 7 | 7 H_3AsO_4 | 4 | 4 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) As_2S_3 | 2 | -2 | -1/2 (Δ[As2S3])/(Δt) KClO_4 | 7 | -7 | -1/7 (Δ[KClO4])/(Δt) H_2SO_4 | 6 | 6 | 1/6 (Δ[H2SO4])/(Δt) KCl | 7 | 7 | 1/7 (Δ[KCl])/(Δt) H_3AsO_4 | 4 | 4 | 1/4 (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) = -1/2 (Δ[As2S3])/(Δt) = -1/7 (Δ[KClO4])/(Δt) = 1/6 (Δ[H2SO4])/(Δt) = 1/7 (Δ[KCl])/(Δt) = 1/4 (Δ[H3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | arsenic(III) sulfide | potassium perchlorate | sulfuric acid | potassium chloride | arsenic acid, solid formula | H_2O | As_2S_3 | KClO_4 | H_2SO_4 | KCl | H_3AsO_4 Hill formula | H_2O | As_2S_3 | ClKO_4 | H_2O_4S | ClK | AsH_3O_4 name | water | arsenic(III) sulfide | potassium perchlorate | sulfuric acid | potassium chloride | arsenic acid, solid IUPAC name | water | | potassium perchlorate | sulfuric acid | potassium chloride | arsoric acid

| water | arsenic(III) sulfide | potassium perchlorate | sulfuric acid | potassium chloride | arsenic acid, solid molar mass | 18.015 g/mol | 246 g/mol | 138.54 g/mol | 98.07 g/mol | 74.55 g/mol | 141.94 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | 300 °C | 400 °C | 10.371 °C | 770 °C | 35.5 °C boiling point | 99.9839 °C | | | 279.6 °C | 1420 °C | 160 °C density | 1 g/cm^3 | 3.43 g/cm^3 | 2.5239 g/cm^3 | 1.8305 g/cm^3 | 1.98 g/cm^3 | 2.2 g/cm^3 solubility in water | | | | very soluble | soluble | surface tension | 0.0728 N/m | | | 0.0735 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.021 Pa s (at 25 °C) | | odor | odorless | | | odorless | odorless |