H2O + HClO4 + As2S3 = H2SO4 + HCl + H3AsO4

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

Balance the chemical equation algebraically: + + ⟶ + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 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 = 2 c_4 + c_5 + 3 c_6 O: | c_1 + 4 c_2 = 4 c_4 + 4 c_6 Cl: | c_2 = c_5 As: | 2 c_3 = c_6 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 = 6 c_2 = 7/2 c_3 = 1 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 = 7 c_3 = 2 c_4 = 6 c_5 = 7 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 + 7 + 2 ⟶ 6 + 7 + 4

+ + ⟶ + +

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

K_c = ([H2SO4]^6 [HCl]^7 [H3AsO4]^4)/([H2O]^12 [HClO4]^7 [As2S3]^2)

rate = -1/12 (Δ[H2O])/(Δt) = -1/7 (Δ[HClO4])/(Δt) = -1/2 (Δ[As2S3])/(Δt) = 1/6 (Δ[H2SO4])/(Δt) = 1/7 (Δ[HCl])/(Δt) = 1/4 (Δ[H3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | perchloric acid | arsenic(III) sulfide | sulfuric acid | hydrogen chloride | arsenic acid, solid Hill formula | H_2O | ClHO_4 | As_2S_3 | H_2O_4S | ClH | AsH_3O_4 name | water | perchloric acid | arsenic(III) sulfide | sulfuric acid | hydrogen chloride | arsenic acid, solid IUPAC name | water | perchloric acid | | sulfuric acid | hydrogen chloride | arsoric acid