HNO3 + Al2S3 = H2O + NO2 + Al2(SO4)3

HNO_3 nitric acid + Al_2S_3 aluminum sulfide ⟶ H_2O water + NO_2 nitrogen dioxide + Al_2(SO_4)_3 aluminum sulfate

Balance the chemical equation algebraically: HNO_3 + Al_2S_3 ⟶ H_2O + NO_2 + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Al_2S_3 ⟶ c_3 H_2O + c_4 NO_2 + c_5 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Al and S: H: | c_1 = 2 c_3 N: | c_1 = c_4 O: | 3 c_1 = c_3 + 2 c_4 + 12 c_5 Al: | 2 c_2 = 2 c_5 S: | 3 c_2 = 3 c_5 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 = 12 c_4 = 24 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 HNO_3 + Al_2S_3 ⟶ 12 H_2O + 24 NO_2 + Al_2(SO_4)_3

+ ⟶ + +

nitric acid + aluminum sulfide ⟶ water + nitrogen dioxide + aluminum sulfate

Construct the equilibrium constant, K, expression for: HNO_3 + Al_2S_3 ⟶ H_2O + NO_2 + Al_2(SO_4)_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: 24 HNO_3 + Al_2S_3 ⟶ 12 H_2O + 24 NO_2 + Al_2(SO_4)_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 HNO_3 | 24 | -24 Al_2S_3 | 1 | -1 H_2O | 12 | 12 NO_2 | 24 | 24 Al_2(SO_4)_3 | 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 | 24 | -24 | ([HNO3])^(-24) Al_2S_3 | 1 | -1 | ([Al2S3])^(-1) H_2O | 12 | 12 | ([H2O])^12 NO_2 | 24 | 24 | ([NO2])^24 Al_2(SO_4)_3 | 1 | 1 | [Al2(SO4)3] 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) ([Al2S3])^(-1) ([H2O])^12 ([NO2])^24 [Al2(SO4)3] = (([H2O])^12 ([NO2])^24 [Al2(SO4)3])/(([HNO3])^24 [Al2S3])

Construct the rate of reaction expression for: HNO_3 + Al_2S_3 ⟶ H_2O + NO_2 + Al_2(SO_4)_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: 24 HNO_3 + Al_2S_3 ⟶ 12 H_2O + 24 NO_2 + Al_2(SO_4)_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 HNO_3 | 24 | -24 Al_2S_3 | 1 | -1 H_2O | 12 | 12 NO_2 | 24 | 24 Al_2(SO_4)_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 HNO_3 | 24 | -24 | -1/24 (Δ[HNO3])/(Δt) Al_2S_3 | 1 | -1 | -(Δ[Al2S3])/(Δt) H_2O | 12 | 12 | 1/12 (Δ[H2O])/(Δt) NO_2 | 24 | 24 | 1/24 (Δ[NO2])/(Δt) Al_2(SO_4)_3 | 1 | 1 | (Δ[Al2(SO4)3])/(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[Al2S3])/(Δt) = 1/12 (Δ[H2O])/(Δt) = 1/24 (Δ[NO2])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | aluminum sulfide | water | nitrogen dioxide | aluminum sulfate formula | HNO_3 | Al_2S_3 | H_2O | NO_2 | Al_2(SO_4)_3 Hill formula | HNO_3 | Al_2S_3 | H_2O | NO_2 | Al_2O_12S_3 name | nitric acid | aluminum sulfide | water | nitrogen dioxide | aluminum sulfate IUPAC name | nitric acid | thioxo-(thioxoalumanylthio)alumane | water | Nitrogen dioxide | dialuminum trisulfate

| nitric acid | aluminum sulfide | water | nitrogen dioxide | aluminum sulfate molar mass | 63.012 g/mol | 150.1 g/mol | 18.015 g/mol | 46.005 g/mol | 342.1 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -41.6 °C | 1100 °C | 0 °C | -11 °C | 770 °C boiling point | 83 °C | 1500 °C | 99.9839 °C | 21 °C | density | 1.5129 g/cm^3 | 2.02 g/cm^3 | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 2.71 g/cm^3 solubility in water | miscible | decomposes | | reacts | soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | odor | | | odorless | |