KOH + Zn + KNO2 = H2O + NH3 + K2ZnO2

KOH potassium hydroxide + Zn zinc + KNO_2 potassium nitrite ⟶ H_2O water + NH_3 ammonia + K2ZnO2

Balance the chemical equation algebraically: KOH + Zn + KNO_2 ⟶ H_2O + NH_3 + K2ZnO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Zn + c_3 KNO_2 ⟶ c_4 H_2O + c_5 NH_3 + c_6 K2ZnO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Zn and N: H: | c_1 = 2 c_4 + 3 c_5 K: | c_1 + c_3 = 2 c_6 O: | c_1 + 2 c_3 = c_4 + 2 c_6 Zn: | c_2 = c_6 N: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 3 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 KOH + 3 Zn + KNO_2 ⟶ H_2O + NH_3 + 3 K2ZnO2

+ + ⟶ + + K2ZnO2

potassium hydroxide + zinc + potassium nitrite ⟶ water + ammonia + K2ZnO2

Construct the equilibrium constant, K, expression for: KOH + Zn + KNO_2 ⟶ H_2O + NH_3 + K2ZnO2 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: 5 KOH + 3 Zn + KNO_2 ⟶ H_2O + NH_3 + 3 K2ZnO2 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 | 5 | -5 Zn | 3 | -3 KNO_2 | 1 | -1 H_2O | 1 | 1 NH_3 | 1 | 1 K2ZnO2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 5 | -5 | ([KOH])^(-5) Zn | 3 | -3 | ([Zn])^(-3) KNO_2 | 1 | -1 | ([KNO2])^(-1) H_2O | 1 | 1 | [H2O] NH_3 | 1 | 1 | [NH3] K2ZnO2 | 3 | 3 | ([K2ZnO2])^3 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])^(-5) ([Zn])^(-3) ([KNO2])^(-1) [H2O] [NH3] ([K2ZnO2])^3 = ([H2O] [NH3] ([K2ZnO2])^3)/(([KOH])^5 ([Zn])^3 [KNO2])

Construct the rate of reaction expression for: KOH + Zn + KNO_2 ⟶ H_2O + NH_3 + K2ZnO2 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: 5 KOH + 3 Zn + KNO_2 ⟶ H_2O + NH_3 + 3 K2ZnO2 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 | 5 | -5 Zn | 3 | -3 KNO_2 | 1 | -1 H_2O | 1 | 1 NH_3 | 1 | 1 K2ZnO2 | 3 | 3 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 | 5 | -5 | -1/5 (Δ[KOH])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) KNO_2 | 1 | -1 | -(Δ[KNO2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(Δt) K2ZnO2 | 3 | 3 | 1/3 (Δ[K2ZnO2])/(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 = -1/5 (Δ[KOH])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -(Δ[KNO2])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NH3])/(Δt) = 1/3 (Δ[K2ZnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | zinc | potassium nitrite | water | ammonia | K2ZnO2 formula | KOH | Zn | KNO_2 | H_2O | NH_3 | K2ZnO2 Hill formula | HKO | Zn | KNO_2 | H_2O | H_3N | K2O2Zn name | potassium hydroxide | zinc | potassium nitrite | water | ammonia |