H2O + HNO2 = H2 + HNO3 + NO

H_2O water + HNO_2 nitrous acid ⟶ H_2 hydrogen + HNO_3 nitric acid + NO nitric oxide

Balance the chemical equation algebraically: H_2O + HNO_2 ⟶ H_2 + HNO_3 + NO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_2 ⟶ c_3 H_2 + c_4 HNO_3 + c_5 NO Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and N: H: | 2 c_1 + c_2 = 2 c_3 + c_4 O: | c_1 + 2 c_2 = 3 c_4 + c_5 N: | c_2 = c_4 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_3 = c_2/4 + 3/4 c_4 = c_2/2 + 1/2 c_5 = c_2/2 - 1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 5 and solve for the remaining coefficients: c_1 = 1 c_2 = 5 c_3 = 2 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 5 HNO_2 ⟶ 2 H_2 + 3 HNO_3 + 2 NO

+ ⟶ + +

water + nitrous acid ⟶ hydrogen + nitric acid + nitric oxide

Construct the equilibrium constant, K, expression for: H_2O + HNO_2 ⟶ H_2 + HNO_3 + NO 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: H_2O + 5 HNO_2 ⟶ 2 H_2 + 3 HNO_3 + 2 NO 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_2O | 1 | -1 HNO_2 | 5 | -5 H_2 | 2 | 2 HNO_3 | 3 | 3 NO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) HNO_2 | 5 | -5 | ([HNO2])^(-5) H_2 | 2 | 2 | ([H2])^2 HNO_3 | 3 | 3 | ([HNO3])^3 NO | 2 | 2 | ([NO])^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 = ([H2O])^(-1) ([HNO2])^(-5) ([H2])^2 ([HNO3])^3 ([NO])^2 = (([H2])^2 ([HNO3])^3 ([NO])^2)/([H2O] ([HNO2])^5)

Construct the rate of reaction expression for: H_2O + HNO_2 ⟶ H_2 + HNO_3 + NO 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: H_2O + 5 HNO_2 ⟶ 2 H_2 + 3 HNO_3 + 2 NO 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_2O | 1 | -1 HNO_2 | 5 | -5 H_2 | 2 | 2 HNO_3 | 3 | 3 NO | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) HNO_2 | 5 | -5 | -1/5 (Δ[HNO2])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) HNO_3 | 3 | 3 | 1/3 (Δ[HNO3])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(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 = -(Δ[H2O])/(Δt) = -1/5 (Δ[HNO2])/(Δt) = 1/2 (Δ[H2])/(Δt) = 1/3 (Δ[HNO3])/(Δt) = 1/2 (Δ[NO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitrous acid | hydrogen | nitric acid | nitric oxide formula | H_2O | HNO_2 | H_2 | HNO_3 | NO name | water | nitrous acid | hydrogen | nitric acid | nitric oxide IUPAC name | water | nitrous acid | molecular hydrogen | nitric acid | nitric oxide