HNO3 + K2SO3 = H2O + K2SO4 + NO2

HNO_3 nitric acid + K_2SO_3 potassium sulfite ⟶ H_2O water + K_2SO_4 potassium sulfate + NO_2 nitrogen dioxide

Balance the chemical equation algebraically: HNO_3 + K_2SO_3 ⟶ H_2O + K_2SO_4 + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 K_2SO_3 ⟶ c_3 H_2O + c_4 K_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, K and S: H: | c_1 = 2 c_3 N: | c_1 = c_5 O: | 3 c_1 + 3 c_2 = c_3 + 4 c_4 + 2 c_5 K: | 2 c_2 = 2 c_4 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + K_2SO_3 ⟶ H_2O + K_2SO_4 + 2 NO_2

+ ⟶ + +

nitric acid + potassium sulfite ⟶ water + potassium sulfate + nitrogen dioxide

Construct the equilibrium constant, K, expression for: HNO_3 + K_2SO_3 ⟶ H_2O + K_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: 2 HNO_3 + K_2SO_3 ⟶ H_2O + K_2SO_4 + 2 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 | 2 | -2 K_2SO_3 | 1 | -1 H_2O | 1 | 1 K_2SO_4 | 1 | 1 NO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) K_2SO_3 | 1 | -1 | ([K2SO3])^(-1) H_2O | 1 | 1 | [H2O] K_2SO_4 | 1 | 1 | [K2SO4] NO_2 | 2 | 2 | ([NO2])^2 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])^(-2) ([K2SO3])^(-1) [H2O] [K2SO4] ([NO2])^2 = ([H2O] [K2SO4] ([NO2])^2)/(([HNO3])^2 [K2SO3])

Construct the rate of reaction expression for: HNO_3 + K_2SO_3 ⟶ H_2O + K_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: 2 HNO_3 + K_2SO_3 ⟶ H_2O + K_2SO_4 + 2 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 | 2 | -2 K_2SO_3 | 1 | -1 H_2O | 1 | 1 K_2SO_4 | 1 | 1 NO_2 | 2 | 2 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 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) K_2SO_3 | 1 | -1 | -(Δ[K2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) NO_2 | 2 | 2 | 1/2 (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 = -1/2 (Δ[HNO3])/(Δt) = -(Δ[K2SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | potassium sulfite | water | potassium sulfate | nitrogen dioxide formula | HNO_3 | K_2SO_3 | H_2O | K_2SO_4 | NO_2 Hill formula | HNO_3 | K_2O_3S | H_2O | K_2O_4S | NO_2 name | nitric acid | potassium sulfite | water | potassium sulfate | nitrogen dioxide IUPAC name | nitric acid | dipotassium sulfite | water | dipotassium sulfate | Nitrogen dioxide