HCl + As2O3 = H2O + AsCl3

HCl hydrogen chloride + As_2O_3 arsenic trioxide ⟶ H_2O water + AsCl_3 arsenic trichloride

Balance the chemical equation algebraically: HCl + As_2O_3 ⟶ H_2O + AsCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 As_2O_3 ⟶ c_3 H_2O + c_4 AsCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, As and O: Cl: | c_1 = 3 c_4 H: | c_1 = 2 c_3 As: | 2 c_2 = c_4 O: | 3 c_2 = c_3 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 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + As_2O_3 ⟶ 3 H_2O + 2 AsCl_3

+ ⟶ +

hydrogen chloride + arsenic trioxide ⟶ water + arsenic trichloride

Construct the equilibrium constant, K, expression for: HCl + As_2O_3 ⟶ H_2O + AsCl_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: 6 HCl + As_2O_3 ⟶ 3 H_2O + 2 AsCl_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 HCl | 6 | -6 As_2O_3 | 1 | -1 H_2O | 3 | 3 AsCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) As_2O_3 | 1 | -1 | ([As2O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 AsCl_3 | 2 | 2 | ([AsCl3])^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 = ([HCl])^(-6) ([As2O3])^(-1) ([H2O])^3 ([AsCl3])^2 = (([H2O])^3 ([AsCl3])^2)/(([HCl])^6 [As2O3])

Construct the rate of reaction expression for: HCl + As_2O_3 ⟶ H_2O + AsCl_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: 6 HCl + As_2O_3 ⟶ 3 H_2O + 2 AsCl_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 HCl | 6 | -6 As_2O_3 | 1 | -1 H_2O | 3 | 3 AsCl_3 | 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 HCl | 6 | -6 | -1/6 (Δ[HCl])/(Δt) As_2O_3 | 1 | -1 | -(Δ[As2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) AsCl_3 | 2 | 2 | 1/2 (Δ[AsCl3])/(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 = -1/6 (Δ[HCl])/(Δt) = -(Δ[As2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[AsCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | arsenic trioxide | water | arsenic trichloride formula | HCl | As_2O_3 | H_2O | AsCl_3 Hill formula | ClH | As_2O_3 | H_2O | AsCl_3 name | hydrogen chloride | arsenic trioxide | water | arsenic trichloride IUPAC name | hydrogen chloride | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | water | trichloroarsane