NH3 + NaClO = H2O + NaCl + N2H4

NH_3 (ammonia) + NaOCl (sodium hypochlorite) ⟶ H_2O (water) + NaCl (sodium chloride) + NH_2NH_2 (diazane)

Balance the chemical equation algebraically: NH_3 + NaOCl ⟶ H_2O + NaCl + NH_2NH_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 NaOCl ⟶ c_3 H_2O + c_4 NaCl + c_5 NH_2NH_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, Cl, Na and O: H: | 3 c_1 = 2 c_3 + 4 c_5 N: | c_1 = 2 c_5 Cl: | c_2 = c_4 Na: | c_2 = c_4 O: | c_2 = c_3 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_3 + NaOCl ⟶ H_2O + NaCl + NH_2NH_2

+ ⟶ + +

ammonia + sodium hypochlorite ⟶ water + sodium chloride + diazane

Construct the equilibrium constant, K, expression for: NH_3 + NaOCl ⟶ H_2O + NaCl + NH_2NH_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 NH_3 + NaOCl ⟶ H_2O + NaCl + NH_2NH_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 NH_3 | 2 | -2 NaOCl | 1 | -1 H_2O | 1 | 1 NaCl | 1 | 1 NH_2NH_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 2 | -2 | ([NH3])^(-2) NaOCl | 1 | -1 | ([NaOCl])^(-1) H_2O | 1 | 1 | [H2O] NaCl | 1 | 1 | [NaCl] NH_2NH_2 | 1 | 1 | [NH2NH2] 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 = ([NH3])^(-2) ([NaOCl])^(-1) [H2O] [NaCl] [NH2NH2] = ([H2O] [NaCl] [NH2NH2])/(([NH3])^2 [NaOCl])

Construct the rate of reaction expression for: NH_3 + NaOCl ⟶ H_2O + NaCl + NH_2NH_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 NH_3 + NaOCl ⟶ H_2O + NaCl + NH_2NH_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 NH_3 | 2 | -2 NaOCl | 1 | -1 H_2O | 1 | 1 NaCl | 1 | 1 NH_2NH_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 NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) NaOCl | 1 | -1 | -(Δ[NaOCl])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NaCl | 1 | 1 | (Δ[NaCl])/(Δt) NH_2NH_2 | 1 | 1 | (Δ[NH2NH2])/(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[NH3])/(Δt) = -(Δ[NaOCl])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NaCl])/(Δt) = (Δ[NH2NH2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | sodium hypochlorite | water | sodium chloride | diazane formula | NH_3 | NaOCl | H_2O | NaCl | NH_2NH_2 Hill formula | H_3N | ClNaO | H_2O | ClNa | H_4N_2 name | ammonia | sodium hypochlorite | water | sodium chloride | diazane IUPAC name | ammonia | sodium hypochlorite | water | sodium chloride | hydrazine