HClO + NH2OH = H2O + HCl + N2

HOCl hypochlorous acid + NH_2OH hydroxylamine ⟶ H_2O water + HCl hydrogen chloride + N_2 nitrogen

Balance the chemical equation algebraically: HOCl + NH_2OH ⟶ H_2O + HCl + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HOCl + c_2 NH_2OH ⟶ c_3 H_2O + c_4 HCl + c_5 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, O and N: Cl: | c_1 = c_4 H: | c_1 + 3 c_2 = 2 c_3 + c_4 O: | c_1 + c_2 = c_3 N: | c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 3 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HOCl + 2 NH_2OH ⟶ 3 H_2O + HCl + N_2

+ ⟶ + +

hypochlorous acid + hydroxylamine ⟶ water + hydrogen chloride + nitrogen

Construct the equilibrium constant, K, expression for: HOCl + NH_2OH ⟶ H_2O + HCl + N_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: HOCl + 2 NH_2OH ⟶ 3 H_2O + HCl + N_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 HOCl | 1 | -1 NH_2OH | 2 | -2 H_2O | 3 | 3 HCl | 1 | 1 N_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HOCl | 1 | -1 | ([HOCl])^(-1) NH_2OH | 2 | -2 | ([NH2OH])^(-2) H_2O | 3 | 3 | ([H2O])^3 HCl | 1 | 1 | [HCl] N_2 | 1 | 1 | [N2] 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 = ([HOCl])^(-1) ([NH2OH])^(-2) ([H2O])^3 [HCl] [N2] = (([H2O])^3 [HCl] [N2])/([HOCl] ([NH2OH])^2)

Construct the rate of reaction expression for: HOCl + NH_2OH ⟶ H_2O + HCl + N_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: HOCl + 2 NH_2OH ⟶ 3 H_2O + HCl + N_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 HOCl | 1 | -1 NH_2OH | 2 | -2 H_2O | 3 | 3 HCl | 1 | 1 N_2 | 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 HOCl | 1 | -1 | -(Δ[HOCl])/(Δt) NH_2OH | 2 | -2 | -1/2 (Δ[NH2OH])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) HCl | 1 | 1 | (Δ[HCl])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(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[HOCl])/(Δt) = -1/2 (Δ[NH2OH])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[HCl])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hypochlorous acid | hydroxylamine | water | hydrogen chloride | nitrogen formula | HOCl | NH_2OH | H_2O | HCl | N_2 Hill formula | ClHO | H_3NO | H_2O | ClH | N_2 name | hypochlorous acid | hydroxylamine | water | hydrogen chloride | nitrogen IUPAC name | hypochlorous acid | hydroxylamine | water | hydrogen chloride | molecular nitrogen