H2O + HNO3 + As2S3 = H2SO4 + NO + H3As4

H_2O water + HNO_3 nitric acid + As_2S_3 arsenic(III) sulfide ⟶ H_2SO_4 sulfuric acid + NO nitric oxide + H3As4

Balance the chemical equation algebraically: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + H3As4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_3 + c_3 As_2S_3 ⟶ c_4 H_2SO_4 + c_5 NO + c_6 H3As4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, As and S: H: | 2 c_1 + c_2 = 2 c_4 + 3 c_6 O: | c_1 + 3 c_2 = 4 c_4 + c_5 N: | c_2 = c_5 As: | 2 c_3 = 4 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 11 c_3 = 2 c_4 = 6 c_5 = 11 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 11 HNO_3 + 2 As_2S_3 ⟶ 6 H_2SO_4 + 11 NO + H3As4

+ + ⟶ + + H3As4

water + nitric acid + arsenic(III) sulfide ⟶ sulfuric acid + nitric oxide + H3As4

Construct the equilibrium constant, K, expression for: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + H3As4 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: 2 H_2O + 11 HNO_3 + 2 As_2S_3 ⟶ 6 H_2SO_4 + 11 NO + H3As4 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 | 2 | -2 HNO_3 | 11 | -11 As_2S_3 | 2 | -2 H_2SO_4 | 6 | 6 NO | 11 | 11 H3As4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) HNO_3 | 11 | -11 | ([HNO3])^(-11) As_2S_3 | 2 | -2 | ([As2S3])^(-2) H_2SO_4 | 6 | 6 | ([H2SO4])^6 NO | 11 | 11 | ([NO])^11 H3As4 | 1 | 1 | [H3As4] 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])^(-2) ([HNO3])^(-11) ([As2S3])^(-2) ([H2SO4])^6 ([NO])^11 [H3As4] = (([H2SO4])^6 ([NO])^11 [H3As4])/(([H2O])^2 ([HNO3])^11 ([As2S3])^2)

Construct the rate of reaction expression for: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + H3As4 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: 2 H_2O + 11 HNO_3 + 2 As_2S_3 ⟶ 6 H_2SO_4 + 11 NO + H3As4 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 | 2 | -2 HNO_3 | 11 | -11 As_2S_3 | 2 | -2 H_2SO_4 | 6 | 6 NO | 11 | 11 H3As4 | 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_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) HNO_3 | 11 | -11 | -1/11 (Δ[HNO3])/(Δt) As_2S_3 | 2 | -2 | -1/2 (Δ[As2S3])/(Δt) H_2SO_4 | 6 | 6 | 1/6 (Δ[H2SO4])/(Δt) NO | 11 | 11 | 1/11 (Δ[NO])/(Δt) H3As4 | 1 | 1 | (Δ[H3As4])/(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 = -1/2 (Δ[H2O])/(Δt) = -1/11 (Δ[HNO3])/(Δt) = -1/2 (Δ[As2S3])/(Δt) = 1/6 (Δ[H2SO4])/(Δt) = 1/11 (Δ[NO])/(Δt) = (Δ[H3As4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitric acid | arsenic(III) sulfide | sulfuric acid | nitric oxide | H3As4 formula | H_2O | HNO_3 | As_2S_3 | H_2SO_4 | NO | H3As4 Hill formula | H_2O | HNO_3 | As_2S_3 | H_2O_4S | NO | H3As4 name | water | nitric acid | arsenic(III) sulfide | sulfuric acid | nitric oxide |

| water | nitric acid | arsenic(III) sulfide | sulfuric acid | nitric oxide | H3As4 molar mass | 18.015 g/mol | 63.012 g/mol | 246 g/mol | 98.07 g/mol | 30.006 g/mol | 302.71 g/mol phase | liquid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | 0 °C | -41.6 °C | 300 °C | 10.371 °C | -163.6 °C | boiling point | 99.9839 °C | 83 °C | | 279.6 °C | -151.7 °C | density | 1 g/cm^3 | 1.5129 g/cm^3 | 3.43 g/cm^3 | 1.8305 g/cm^3 | 0.001226 g/cm^3 (at 25 °C) | solubility in water | | miscible | | very soluble | | surface tension | 0.0728 N/m | | | 0.0735 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 25 °C) | | 0.021 Pa s (at 25 °C) | 1.911×10^-5 Pa s (at 25 °C) | odor | odorless | | | odorless | |