HNO3 + Sb2S3 = H2O + SO2 + NO + H3SbO4

HNO_3 nitric acid + Sb_2S_3 antimony(III) sulfide ⟶ H_2O water + SO_2 sulfur dioxide + NO nitric oxide + H3SbO4

Balance the chemical equation algebraically: HNO_3 + Sb_2S_3 ⟶ H_2O + SO_2 + NO + H3SbO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Sb_2S_3 ⟶ c_3 H_2O + c_4 SO_2 + c_5 NO + c_6 H3SbO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, S and Sb: H: | c_1 = 2 c_3 + 3 c_6 N: | c_1 = c_5 O: | 3 c_1 = c_3 + 2 c_4 + c_5 + 4 c_6 S: | 3 c_2 = c_4 Sb: | 2 c_2 = c_6 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 = 11 c_2 = 3/2 c_3 = 1 c_4 = 9/2 c_5 = 11 c_6 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 22 c_2 = 3 c_3 = 2 c_4 = 9 c_5 = 22 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 22 HNO_3 + 3 Sb_2S_3 ⟶ 2 H_2O + 9 SO_2 + 22 NO + 6 H3SbO4

+ ⟶ + + + H3SbO4

nitric acid + antimony(III) sulfide ⟶ water + sulfur dioxide + nitric oxide + H3SbO4

Construct the equilibrium constant, K, expression for: HNO_3 + Sb_2S_3 ⟶ H_2O + SO_2 + NO + H3SbO4 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: 22 HNO_3 + 3 Sb_2S_3 ⟶ 2 H_2O + 9 SO_2 + 22 NO + 6 H3SbO4 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 | 22 | -22 Sb_2S_3 | 3 | -3 H_2O | 2 | 2 SO_2 | 9 | 9 NO | 22 | 22 H3SbO4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 22 | -22 | ([HNO3])^(-22) Sb_2S_3 | 3 | -3 | ([Sb2S3])^(-3) H_2O | 2 | 2 | ([H2O])^2 SO_2 | 9 | 9 | ([SO2])^9 NO | 22 | 22 | ([NO])^22 H3SbO4 | 6 | 6 | ([H3SbO4])^6 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])^(-22) ([Sb2S3])^(-3) ([H2O])^2 ([SO2])^9 ([NO])^22 ([H3SbO4])^6 = (([H2O])^2 ([SO2])^9 ([NO])^22 ([H3SbO4])^6)/(([HNO3])^22 ([Sb2S3])^3)

Construct the rate of reaction expression for: HNO_3 + Sb_2S_3 ⟶ H_2O + SO_2 + NO + H3SbO4 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: 22 HNO_3 + 3 Sb_2S_3 ⟶ 2 H_2O + 9 SO_2 + 22 NO + 6 H3SbO4 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 | 22 | -22 Sb_2S_3 | 3 | -3 H_2O | 2 | 2 SO_2 | 9 | 9 NO | 22 | 22 H3SbO4 | 6 | 6 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 | 22 | -22 | -1/22 (Δ[HNO3])/(Δt) Sb_2S_3 | 3 | -3 | -1/3 (Δ[Sb2S3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) SO_2 | 9 | 9 | 1/9 (Δ[SO2])/(Δt) NO | 22 | 22 | 1/22 (Δ[NO])/(Δt) H3SbO4 | 6 | 6 | 1/6 (Δ[H3SbO4])/(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 = -1/22 (Δ[HNO3])/(Δt) = -1/3 (Δ[Sb2S3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/9 (Δ[SO2])/(Δt) = 1/22 (Δ[NO])/(Δt) = 1/6 (Δ[H3SbO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | antimony(III) sulfide | water | sulfur dioxide | nitric oxide | H3SbO4 formula | HNO_3 | Sb_2S_3 | H_2O | SO_2 | NO | H3SbO4 Hill formula | HNO_3 | S_3Sb_2 | H_2O | O_2S | NO | H3O4Sb name | nitric acid | antimony(III) sulfide | water | sulfur dioxide | nitric oxide | IUPAC name | nitric acid | thioxo-(thioxostibanylthio)stibane | water | sulfur dioxide | nitric oxide |