HNO3 + Sb2S3 = H2O + S + NO2 + Sb2O5

HNO_3 nitric acid + Sb_2S_3 antimony(III) sulfide ⟶ H_2O water + S mixed sulfur + NO_2 nitrogen dioxide + Sb_2O_5 antimony pentoxide

Balance the chemical equation algebraically: HNO_3 + Sb_2S_3 ⟶ H_2O + S + NO_2 + Sb_2O_5 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 S + c_5 NO_2 + c_6 Sb_2O_5 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 N: | c_1 = c_5 O: | 3 c_1 = c_3 + 2 c_5 + 5 c_6 S: | 3 c_2 = c_4 Sb: | 2 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 1 c_3 = 5 c_4 = 3 c_5 = 10 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + Sb_2S_3 ⟶ 5 H_2O + 3 S + 10 NO_2 + Sb_2O_5

+ ⟶ + + +

nitric acid + antimony(III) sulfide ⟶ water + mixed sulfur + nitrogen dioxide + antimony pentoxide

Construct the equilibrium constant, K, expression for: HNO_3 + Sb_2S_3 ⟶ H_2O + S + NO_2 + Sb_2O_5 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: 10 HNO_3 + Sb_2S_3 ⟶ 5 H_2O + 3 S + 10 NO_2 + Sb_2O_5 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 | 10 | -10 Sb_2S_3 | 1 | -1 H_2O | 5 | 5 S | 3 | 3 NO_2 | 10 | 10 Sb_2O_5 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 10 | -10 | ([HNO3])^(-10) Sb_2S_3 | 1 | -1 | ([Sb2S3])^(-1) H_2O | 5 | 5 | ([H2O])^5 S | 3 | 3 | ([S])^3 NO_2 | 10 | 10 | ([NO2])^10 Sb_2O_5 | 1 | 1 | [Sb2O5] 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])^(-10) ([Sb2S3])^(-1) ([H2O])^5 ([S])^3 ([NO2])^10 [Sb2O5] = (([H2O])^5 ([S])^3 ([NO2])^10 [Sb2O5])/(([HNO3])^10 [Sb2S3])

Construct the rate of reaction expression for: HNO_3 + Sb_2S_3 ⟶ H_2O + S + NO_2 + Sb_2O_5 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: 10 HNO_3 + Sb_2S_3 ⟶ 5 H_2O + 3 S + 10 NO_2 + Sb_2O_5 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 | 10 | -10 Sb_2S_3 | 1 | -1 H_2O | 5 | 5 S | 3 | 3 NO_2 | 10 | 10 Sb_2O_5 | 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 HNO_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) Sb_2S_3 | 1 | -1 | -(Δ[Sb2S3])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) NO_2 | 10 | 10 | 1/10 (Δ[NO2])/(Δt) Sb_2O_5 | 1 | 1 | (Δ[Sb2O5])/(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 = -1/10 (Δ[HNO3])/(Δt) = -(Δ[Sb2S3])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/10 (Δ[NO2])/(Δt) = (Δ[Sb2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | antimony(III) sulfide | water | mixed sulfur | nitrogen dioxide | antimony pentoxide formula | HNO_3 | Sb_2S_3 | H_2O | S | NO_2 | Sb_2O_5 Hill formula | HNO_3 | S_3Sb_2 | H_2O | S | NO_2 | O_5Sb_2 name | nitric acid | antimony(III) sulfide | water | mixed sulfur | nitrogen dioxide | antimony pentoxide IUPAC name | nitric acid | thioxo-(thioxostibanylthio)stibane | water | sulfur | Nitrogen dioxide |