SO2 + NH3 = H2O + S + NO2

SO_2 sulfur dioxide + NH_3 ammonia ⟶ H_2O water + S mixed sulfur + NO_2 nitrogen dioxide

Balance the chemical equation algebraically: SO_2 + NH_3 ⟶ H_2O + S + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 NH_3 ⟶ c_3 H_2O + c_4 S + c_5 NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S, H and N: O: | 2 c_1 = c_3 + 2 c_5 S: | c_1 = c_4 H: | 3 c_2 = 2 c_3 N: | c_2 = 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 = 7/4 c_2 = 1 c_3 = 3/2 c_4 = 7/4 c_5 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 7 c_2 = 4 c_3 = 6 c_4 = 7 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 SO_2 + 4 NH_3 ⟶ 6 H_2O + 7 S + 4 NO_2

+ ⟶ + +

sulfur dioxide + ammonia ⟶ water + mixed sulfur + nitrogen dioxide

Construct the equilibrium constant, K, expression for: SO_2 + NH_3 ⟶ H_2O + S + NO_2 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: 7 SO_2 + 4 NH_3 ⟶ 6 H_2O + 7 S + 4 NO_2 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 SO_2 | 7 | -7 NH_3 | 4 | -4 H_2O | 6 | 6 S | 7 | 7 NO_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 7 | -7 | ([SO2])^(-7) NH_3 | 4 | -4 | ([NH3])^(-4) H_2O | 6 | 6 | ([H2O])^6 S | 7 | 7 | ([S])^7 NO_2 | 4 | 4 | ([NO2])^4 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 = ([SO2])^(-7) ([NH3])^(-4) ([H2O])^6 ([S])^7 ([NO2])^4 = (([H2O])^6 ([S])^7 ([NO2])^4)/(([SO2])^7 ([NH3])^4)

Construct the rate of reaction expression for: SO_2 + NH_3 ⟶ H_2O + S + NO_2 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: 7 SO_2 + 4 NH_3 ⟶ 6 H_2O + 7 S + 4 NO_2 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 SO_2 | 7 | -7 NH_3 | 4 | -4 H_2O | 6 | 6 S | 7 | 7 NO_2 | 4 | 4 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 SO_2 | 7 | -7 | -1/7 (Δ[SO2])/(Δt) NH_3 | 4 | -4 | -1/4 (Δ[NH3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) S | 7 | 7 | 1/7 (Δ[S])/(Δt) NO_2 | 4 | 4 | 1/4 (Δ[NO2])/(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 = -1/7 (Δ[SO2])/(Δt) = -1/4 (Δ[NH3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/7 (Δ[S])/(Δt) = 1/4 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | ammonia | water | mixed sulfur | nitrogen dioxide formula | SO_2 | NH_3 | H_2O | S | NO_2 Hill formula | O_2S | H_3N | H_2O | S | NO_2 name | sulfur dioxide | ammonia | water | mixed sulfur | nitrogen dioxide IUPAC name | sulfur dioxide | ammonia | water | sulfur | Nitrogen dioxide