HNO3 + S = H2O + H2SO4 + NO2

HNO_3 (nitric acid) + S (mixed sulfur) ⟶ H_2O (water) + H_2SO_4 (sulfuric acid) + NO_2 (nitrogen dioxide)

Balance the chemical equation algebraically: HNO_3 + S ⟶ H_2O + H_2SO_4 + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 S ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and S: H: | c_1 = 2 c_3 + 2 c_4 N: | c_1 = c_5 O: | 3 c_1 = c_3 + 4 c_4 + 2 c_5 S: | 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 = 6 c_2 = 1 c_3 = 2 c_4 = 1 c_5 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HNO_3 + S ⟶ 2 H_2O + H_2SO_4 + 6 NO_2

+ ⟶ + +

nitric acid + mixed sulfur ⟶ water + sulfuric acid + nitrogen dioxide

Construct the equilibrium constant, K, expression for: HNO_3 + S ⟶ H_2O + H_2SO_4 + 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: 6 HNO_3 + S ⟶ 2 H_2O + H_2SO_4 + 6 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 HNO_3 | 6 | -6 S | 1 | -1 H_2O | 2 | 2 H_2SO_4 | 1 | 1 NO_2 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 6 | -6 | ([HNO3])^(-6) S | 1 | -1 | ([S])^(-1) H_2O | 2 | 2 | ([H2O])^2 H_2SO_4 | 1 | 1 | [H2SO4] NO_2 | 6 | 6 | ([NO2])^6 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])^(-6) ([S])^(-1) ([H2O])^2 [H2SO4] ([NO2])^6 = (([H2O])^2 [H2SO4] ([NO2])^6)/(([HNO3])^6 [S])

Construct the rate of reaction expression for: HNO_3 + S ⟶ H_2O + H_2SO_4 + 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: 6 HNO_3 + S ⟶ 2 H_2O + H_2SO_4 + 6 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 HNO_3 | 6 | -6 S | 1 | -1 H_2O | 2 | 2 H_2SO_4 | 1 | 1 NO_2 | 6 | 6 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 | 6 | -6 | -1/6 (Δ[HNO3])/(Δt) S | 1 | -1 | -(Δ[S])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NO_2 | 6 | 6 | 1/6 (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 = -1/6 (Δ[HNO3])/(Δt) = -(Δ[S])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[H2SO4])/(Δt) = 1/6 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | mixed sulfur | water | sulfuric acid | nitrogen dioxide formula | HNO_3 | S | H_2O | H_2SO_4 | NO_2 Hill formula | HNO_3 | S | H_2O | H_2O_4S | NO_2 name | nitric acid | mixed sulfur | water | sulfuric acid | nitrogen dioxide IUPAC name | nitric acid | sulfur | water | sulfuric acid | Nitrogen dioxide