HNO3 + As2S3 = H2O + SO2 + NO2 + H2AsO4

HNO_3 nitric acid + As_2S_3 arsenic(III) sulfide ⟶ H_2O water + SO_2 sulfur dioxide + NO_2 nitrogen dioxide + H2AsO4

Balance the chemical equation algebraically: HNO_3 + As_2S_3 ⟶ H_2O + SO_2 + NO_2 + H2AsO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 As_2S_3 ⟶ c_3 H_2O + c_4 SO_2 + c_5 NO_2 + c_6 H2AsO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, As and S: H: | c_1 = 2 c_3 + 2 c_6 N: | c_1 = c_5 O: | 3 c_1 = c_3 + 2 c_4 + 2 c_5 + 4 c_6 As: | 2 c_2 = c_6 S: | 3 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 24 c_2 = 1 c_3 = 10 c_4 = 3 c_5 = 24 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 HNO_3 + As_2S_3 ⟶ 10 H_2O + 3 SO_2 + 24 NO_2 + 2 H2AsO4

+ ⟶ + + + H2AsO4

nitric acid + arsenic(III) sulfide ⟶ water + sulfur dioxide + nitrogen dioxide + H2AsO4

Construct the equilibrium constant, K, expression for: HNO_3 + As_2S_3 ⟶ H_2O + SO_2 + NO_2 + H2AsO4 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: 24 HNO_3 + As_2S_3 ⟶ 10 H_2O + 3 SO_2 + 24 NO_2 + 2 H2AsO4 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 HNO_3 | 24 | -24 As_2S_3 | 1 | -1 H_2O | 10 | 10 SO_2 | 3 | 3 NO_2 | 24 | 24 H2AsO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 24 | -24 | ([HNO3])^(-24) As_2S_3 | 1 | -1 | ([As2S3])^(-1) H_2O | 10 | 10 | ([H2O])^10 SO_2 | 3 | 3 | ([SO2])^3 NO_2 | 24 | 24 | ([NO2])^24 H2AsO4 | 2 | 2 | ([H2AsO4])^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 = ([HNO3])^(-24) ([As2S3])^(-1) ([H2O])^10 ([SO2])^3 ([NO2])^24 ([H2AsO4])^2 = (([H2O])^10 ([SO2])^3 ([NO2])^24 ([H2AsO4])^2)/(([HNO3])^24 [As2S3])

Construct the rate of reaction expression for: HNO_3 + As_2S_3 ⟶ H_2O + SO_2 + NO_2 + H2AsO4 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: 24 HNO_3 + As_2S_3 ⟶ 10 H_2O + 3 SO_2 + 24 NO_2 + 2 H2AsO4 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 HNO_3 | 24 | -24 As_2S_3 | 1 | -1 H_2O | 10 | 10 SO_2 | 3 | 3 NO_2 | 24 | 24 H2AsO4 | 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 HNO_3 | 24 | -24 | -1/24 (Δ[HNO3])/(Δt) As_2S_3 | 1 | -1 | -(Δ[As2S3])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) NO_2 | 24 | 24 | 1/24 (Δ[NO2])/(Δt) H2AsO4 | 2 | 2 | 1/2 (Δ[H2AsO4])/(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 = -1/24 (Δ[HNO3])/(Δt) = -(Δ[As2S3])/(Δt) = 1/10 (Δ[H2O])/(Δt) = 1/3 (Δ[SO2])/(Δt) = 1/24 (Δ[NO2])/(Δt) = 1/2 (Δ[H2AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | arsenic(III) sulfide | water | sulfur dioxide | nitrogen dioxide | H2AsO4 formula | HNO_3 | As_2S_3 | H_2O | SO_2 | NO_2 | H2AsO4 Hill formula | HNO_3 | As_2S_3 | H_2O | O_2S | NO_2 | H2AsO4 name | nitric acid | arsenic(III) sulfide | water | sulfur dioxide | nitrogen dioxide | IUPAC name | nitric acid | | water | sulfur dioxide | Nitrogen dioxide |