HNO2 + HN3 = H2O + N2 + N2O

HNO_2 nitrous acid + HNN congruent N hydrazoic acid ⟶ H_2O water + N_2 nitrogen + N_2O nitrous oxide

Balance the chemical equation algebraically: HNO_2 + HNN congruent N ⟶ H_2O + N_2 + N_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_2 + c_2 HNN congruent N ⟶ c_3 H_2O + c_4 N_2 + c_5 N_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, N and O: H: | c_1 + c_2 = 2 c_3 N: | c_1 + 3 c_2 = 2 c_4 + 2 c_5 O: | 2 c_1 = c_3 + 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_2/2 + 1/2 c_4 = 2 c_2 - 1 c_5 = 3/2 - c_2/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 1 and solve for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HNO_2 + HNN congruent N ⟶ H_2O + N_2 + N_2O

+ ⟶ + +

nitrous acid + hydrazoic acid ⟶ water + nitrogen + nitrous oxide

Construct the equilibrium constant, K, expression for: HNO_2 + HNN congruent N ⟶ H_2O + N_2 + N_2O 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: HNO_2 + HNN congruent N ⟶ H_2O + N_2 + N_2O 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_2 | 1 | -1 HNN congruent N | 1 | -1 H_2O | 1 | 1 N_2 | 1 | 1 N_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_2 | 1 | -1 | ([HNO2])^(-1) HNN congruent N | 1 | -1 | ([HNN congruent N])^(-1) H_2O | 1 | 1 | [H2O] N_2 | 1 | 1 | [N2] N_2O | 1 | 1 | [N2O] 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 = ([HNO2])^(-1) ([HNN congruent N])^(-1) [H2O] [N2] [N2O] = ([H2O] [N2] [N2O])/([HNO2] [HNN congruent N])

Construct the rate of reaction expression for: HNO_2 + HNN congruent N ⟶ H_2O + N_2 + N_2O 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: HNO_2 + HNN congruent N ⟶ H_2O + N_2 + N_2O 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_2 | 1 | -1 HNN congruent N | 1 | -1 H_2O | 1 | 1 N_2 | 1 | 1 N_2O | 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 HNO_2 | 1 | -1 | -(Δ[HNO2])/(Δt) HNN congruent N | 1 | -1 | -(Δ[HNN congruent N])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) N_2O | 1 | 1 | (Δ[N2O])/(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[HNO2])/(Δt) = -(Δ[HNN congruent N])/(Δt) = (Δ[H2O])/(Δt) = (Δ[N2])/(Δt) = (Δ[N2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrous acid | hydrazoic acid | water | nitrogen | nitrous oxide formula | HNO_2 | HNN congruent N | H_2O | N_2 | N_2O Hill formula | HNO_2 | HN_3 | H_2O | N_2 | N_2O name | nitrous acid | hydrazoic acid | water | nitrogen | nitrous oxide IUPAC name | nitrous acid | diazonioazanide | water | molecular nitrogen | nitrous oxide