NH4HSO3 = H2O + SO2 + (NH4)2SO3

NH_4HSO_3 ammonium hydrogen sulfite ⟶ H_2O water + SO_2 sulfur dioxide + H_8N_2O_3S ammonium sulfite

Balance the chemical equation algebraically: NH_4HSO_3 ⟶ H_2O + SO_2 + H_8N_2O_3S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4HSO_3 ⟶ c_2 H_2O + c_3 SO_2 + c_4 H_8N_2O_3S Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and S: H: | 5 c_1 = 2 c_2 + 8 c_4 N: | c_1 = 2 c_4 O: | 3 c_1 = c_2 + 2 c_3 + 3 c_4 S: | c_1 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_4HSO_3 ⟶ H_2O + SO_2 + H_8N_2O_3S

⟶ + +

ammonium hydrogen sulfite ⟶ water + sulfur dioxide + ammonium sulfite

Construct the equilibrium constant, K, expression for: NH_4HSO_3 ⟶ H_2O + SO_2 + H_8N_2O_3S 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 NH_4HSO_3 ⟶ H_2O + SO_2 + H_8N_2O_3S 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 NH_4HSO_3 | 2 | -2 H_2O | 1 | 1 SO_2 | 1 | 1 H_8N_2O_3S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4HSO_3 | 2 | -2 | ([NH4HSO3])^(-2) H_2O | 1 | 1 | [H2O] SO_2 | 1 | 1 | [SO2] H_8N_2O_3S | 1 | 1 | [H8N2O3S] 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 = ([NH4HSO3])^(-2) [H2O] [SO2] [H8N2O3S] = ([H2O] [SO2] [H8N2O3S])/([NH4HSO3])^2

Construct the rate of reaction expression for: NH_4HSO_3 ⟶ H_2O + SO_2 + H_8N_2O_3S 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 NH_4HSO_3 ⟶ H_2O + SO_2 + H_8N_2O_3S 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 NH_4HSO_3 | 2 | -2 H_2O | 1 | 1 SO_2 | 1 | 1 H_8N_2O_3S | 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 NH_4HSO_3 | 2 | -2 | -1/2 (Δ[NH4HSO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) H_8N_2O_3S | 1 | 1 | (Δ[H8N2O3S])/(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[NH4HSO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[SO2])/(Δt) = (Δ[H8N2O3S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium hydrogen sulfite | water | sulfur dioxide | ammonium sulfite formula | NH_4HSO_3 | H_2O | SO_2 | H_8N_2O_3S Hill formula | H_5NO_3S | H_2O | O_2S | H_8N_2O_3S name | ammonium hydrogen sulfite | water | sulfur dioxide | ammonium sulfite IUPAC name | | water | sulfur dioxide | diazanium sulfite