H2S + H3AsO3 = H2O + As2S3

H_2S hydrogen sulfide + As(OH)_3 arsenious acid ⟶ H_2O water + As_2S_3 arsenic(III) sulfide

Balance the chemical equation algebraically: H_2S + As(OH)_3 ⟶ H_2O + As_2S_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 As(OH)_3 ⟶ c_3 H_2O + c_4 As_2S_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, As and O: H: | 2 c_1 + 3 c_2 = 2 c_3 S: | c_1 = 3 c_4 As: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2S + 2 As(OH)_3 ⟶ 6 H_2O + As_2S_3

+ ⟶ +

hydrogen sulfide + arsenious acid ⟶ water + arsenic(III) sulfide

Construct the equilibrium constant, K, expression for: H_2S + As(OH)_3 ⟶ H_2O + As_2S_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: 3 H_2S + 2 As(OH)_3 ⟶ 6 H_2O + As_2S_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 H_2S | 3 | -3 As(OH)_3 | 2 | -2 H_2O | 6 | 6 As_2S_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2S | 3 | -3 | ([H2S])^(-3) As(OH)_3 | 2 | -2 | ([As(OH)3])^(-2) H_2O | 6 | 6 | ([H2O])^6 As_2S_3 | 1 | 1 | [As2S3] 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 = ([H2S])^(-3) ([As(OH)3])^(-2) ([H2O])^6 [As2S3] = (([H2O])^6 [As2S3])/(([H2S])^3 ([As(OH)3])^2)

Construct the rate of reaction expression for: H_2S + As(OH)_3 ⟶ H_2O + As_2S_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: 3 H_2S + 2 As(OH)_3 ⟶ 6 H_2O + As_2S_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 H_2S | 3 | -3 As(OH)_3 | 2 | -2 H_2O | 6 | 6 As_2S_3 | 1 | 1 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_2S | 3 | -3 | -1/3 (Δ[H2S])/(Δt) As(OH)_3 | 2 | -2 | -1/2 (Δ[As(OH)3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) As_2S_3 | 1 | 1 | (Δ[As2S3])/(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 = -1/3 (Δ[H2S])/(Δt) = -1/2 (Δ[As(OH)3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[As2S3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | arsenious acid | water | arsenic(III) sulfide formula | H_2S | As(OH)_3 | H_2O | As_2S_3 Hill formula | H_2S | AsH_3O_3 | H_2O | As_2S_3 name | hydrogen sulfide | arsenious acid | water | arsenic(III) sulfide IUPAC name | hydrogen sulfide | arsorous acid | water |

| hydrogen sulfide | arsenious acid | water | arsenic(III) sulfide molar mass | 34.08 g/mol | 125.94 g/mol | 18.015 g/mol | 246 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -85 °C | | 0 °C | 300 °C boiling point | -60 °C | | 99.9839 °C | density | 0.001393 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 3.43 g/cm^3 surface tension | | | 0.0728 N/m | dynamic viscosity | 1.239×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |