KOH + AgNO3 + N2H4 = N2 + KNO3 + Ag + H2O2O

KOH potassium hydroxide + AgNO_3 silver nitrate + NH_2NH_2 diazane ⟶ N_2 nitrogen + KNO_3 potassium nitrate + Ag silver + H2O2O

Balance the chemical equation algebraically: KOH + AgNO_3 + NH_2NH_2 ⟶ N_2 + KNO_3 + Ag + H2O2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 AgNO_3 + c_3 NH_2NH_2 ⟶ c_4 N_2 + c_5 KNO_3 + c_6 Ag + c_7 H2O2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Ag and N: H: | c_1 + 4 c_3 = 2 c_7 K: | c_1 = c_5 O: | c_1 + 3 c_2 = 3 c_5 + 3 c_7 Ag: | c_2 = c_6 N: | c_2 + 2 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = (7 c_1)/6 + 2 c_3 = 1 c_4 = c_1/12 + 2 c_5 = c_1 c_6 = (7 c_1)/6 + 2 c_7 = c_1/2 + 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 12 and solve for the remaining coefficients: c_1 = 12 c_2 = 16 c_3 = 1 c_4 = 3 c_5 = 12 c_6 = 16 c_7 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 KOH + 16 AgNO_3 + NH_2NH_2 ⟶ 3 N_2 + 12 KNO_3 + 16 Ag + 8 H2O2O

+ + ⟶ + + + H2O2O

potassium hydroxide + silver nitrate + diazane ⟶ nitrogen + potassium nitrate + silver + H2O2O

Construct the equilibrium constant, K, expression for: KOH + AgNO_3 + NH_2NH_2 ⟶ N_2 + KNO_3 + Ag + H2O2O 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: 12 KOH + 16 AgNO_3 + NH_2NH_2 ⟶ 3 N_2 + 12 KNO_3 + 16 Ag + 8 H2O2O 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 KOH | 12 | -12 AgNO_3 | 16 | -16 NH_2NH_2 | 1 | -1 N_2 | 3 | 3 KNO_3 | 12 | 12 Ag | 16 | 16 H2O2O | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 12 | -12 | ([KOH])^(-12) AgNO_3 | 16 | -16 | ([AgNO3])^(-16) NH_2NH_2 | 1 | -1 | ([NH2NH2])^(-1) N_2 | 3 | 3 | ([N2])^3 KNO_3 | 12 | 12 | ([KNO3])^12 Ag | 16 | 16 | ([Ag])^16 H2O2O | 8 | 8 | ([H2O2O])^8 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 = ([KOH])^(-12) ([AgNO3])^(-16) ([NH2NH2])^(-1) ([N2])^3 ([KNO3])^12 ([Ag])^16 ([H2O2O])^8 = (([N2])^3 ([KNO3])^12 ([Ag])^16 ([H2O2O])^8)/(([KOH])^12 ([AgNO3])^16 [NH2NH2])

Construct the rate of reaction expression for: KOH + AgNO_3 + NH_2NH_2 ⟶ N_2 + KNO_3 + Ag + H2O2O 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: 12 KOH + 16 AgNO_3 + NH_2NH_2 ⟶ 3 N_2 + 12 KNO_3 + 16 Ag + 8 H2O2O 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 KOH | 12 | -12 AgNO_3 | 16 | -16 NH_2NH_2 | 1 | -1 N_2 | 3 | 3 KNO_3 | 12 | 12 Ag | 16 | 16 H2O2O | 8 | 8 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 KOH | 12 | -12 | -1/12 (Δ[KOH])/(Δt) AgNO_3 | 16 | -16 | -1/16 (Δ[AgNO3])/(Δt) NH_2NH_2 | 1 | -1 | -(Δ[NH2NH2])/(Δt) N_2 | 3 | 3 | 1/3 (Δ[N2])/(Δt) KNO_3 | 12 | 12 | 1/12 (Δ[KNO3])/(Δt) Ag | 16 | 16 | 1/16 (Δ[Ag])/(Δt) H2O2O | 8 | 8 | 1/8 (Δ[H2O2O])/(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 = -1/12 (Δ[KOH])/(Δt) = -1/16 (Δ[AgNO3])/(Δt) = -(Δ[NH2NH2])/(Δt) = 1/3 (Δ[N2])/(Δt) = 1/12 (Δ[KNO3])/(Δt) = 1/16 (Δ[Ag])/(Δt) = 1/8 (Δ[H2O2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | silver nitrate | diazane | nitrogen | potassium nitrate | silver | H2O2O formula | KOH | AgNO_3 | NH_2NH_2 | N_2 | KNO_3 | Ag | H2O2O Hill formula | HKO | AgNO_3 | H_4N_2 | N_2 | KNO_3 | Ag | H2O3 name | potassium hydroxide | silver nitrate | diazane | nitrogen | potassium nitrate | silver | IUPAC name | potassium hydroxide | silver nitrate | hydrazine | molecular nitrogen | potassium nitrate | silver |