(NH4)2SO3 = H2S + NH3 + (NH4)2SO4

H_8N_2O_3S ammonium sulfite ⟶ H_2S hydrogen sulfide + NH_3 ammonia + (NH_4)_2SO_4 ammonium sulfate

Balance the chemical equation algebraically: H_8N_2O_3S ⟶ H_2S + NH_3 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_8N_2O_3S ⟶ c_2 H_2S + c_3 NH_3 + c_4 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and S: H: | 8 c_1 = 2 c_2 + 3 c_3 + 8 c_4 N: | 2 c_1 = c_3 + 2 c_4 O: | 3 c_1 = 4 c_4 S: | c_1 = 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 = 4 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_8N_2O_3S ⟶ H_2S + 2 NH_3 + 3 (NH_4)_2SO_4

⟶ + +

ammonium sulfite ⟶ hydrogen sulfide + ammonia + ammonium sulfate

Construct the equilibrium constant, K, expression for: H_8N_2O_3S ⟶ H_2S + NH_3 + (NH_4)_2SO_4 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: 4 H_8N_2O_3S ⟶ H_2S + 2 NH_3 + 3 (NH_4)_2SO_4 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_8N_2O_3S | 4 | -4 H_2S | 1 | 1 NH_3 | 2 | 2 (NH_4)_2SO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_8N_2O_3S | 4 | -4 | ([H8N2O3S])^(-4) H_2S | 1 | 1 | [H2S] NH_3 | 2 | 2 | ([NH3])^2 (NH_4)_2SO_4 | 3 | 3 | ([(NH4)2SO4])^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 = ([H8N2O3S])^(-4) [H2S] ([NH3])^2 ([(NH4)2SO4])^3 = ([H2S] ([NH3])^2 ([(NH4)2SO4])^3)/([H8N2O3S])^4

Construct the rate of reaction expression for: H_8N_2O_3S ⟶ H_2S + NH_3 + (NH_4)_2SO_4 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: 4 H_8N_2O_3S ⟶ H_2S + 2 NH_3 + 3 (NH_4)_2SO_4 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_8N_2O_3S | 4 | -4 H_2S | 1 | 1 NH_3 | 2 | 2 (NH_4)_2SO_4 | 3 | 3 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_8N_2O_3S | 4 | -4 | -1/4 (Δ[H8N2O3S])/(Δt) H_2S | 1 | 1 | (Δ[H2S])/(Δt) NH_3 | 2 | 2 | 1/2 (Δ[NH3])/(Δt) (NH_4)_2SO_4 | 3 | 3 | 1/3 (Δ[(NH4)2SO4])/(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 = -1/4 (Δ[H8N2O3S])/(Δt) = (Δ[H2S])/(Δt) = 1/2 (Δ[NH3])/(Δt) = 1/3 (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium sulfite | hydrogen sulfide | ammonia | ammonium sulfate formula | H_8N_2O_3S | H_2S | NH_3 | (NH_4)_2SO_4 Hill formula | H_8N_2O_3S | H_2S | H_3N | H_8N_2O_4S name | ammonium sulfite | hydrogen sulfide | ammonia | ammonium sulfate IUPAC name | diazanium sulfite | hydrogen sulfide | ammonia |