H2O + KOH + Al + KNO2 = NH3 + KAlO2

H_2O water + KOH potassium hydroxide + Al aluminum + KNO_2 potassium nitrite ⟶ NH_3 ammonia + KAlO2

Balance the chemical equation algebraically: H_2O + KOH + Al + KNO_2 ⟶ NH_3 + KAlO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KOH + c_3 Al + c_4 KNO_2 ⟶ c_5 NH_3 + c_6 KAlO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Al and N: H: | 2 c_1 + c_2 = 3 c_5 O: | c_1 + c_2 + 2 c_4 = 2 c_6 K: | c_2 + c_4 = c_6 Al: | c_3 = c_6 N: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + KOH + 2 Al + KNO_2 ⟶ NH_3 + 2 KAlO2

+ + + ⟶ + KAlO2

water + potassium hydroxide + aluminum + potassium nitrite ⟶ ammonia + KAlO2

Construct the equilibrium constant, K, expression for: H_2O + KOH + Al + KNO_2 ⟶ NH_3 + KAlO2 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: H_2O + KOH + 2 Al + KNO_2 ⟶ NH_3 + 2 KAlO2 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 H_2O | 1 | -1 KOH | 1 | -1 Al | 2 | -2 KNO_2 | 1 | -1 NH_3 | 1 | 1 KAlO2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) KOH | 1 | -1 | ([KOH])^(-1) Al | 2 | -2 | ([Al])^(-2) KNO_2 | 1 | -1 | ([KNO2])^(-1) NH_3 | 1 | 1 | [NH3] KAlO2 | 2 | 2 | ([KAlO2])^2 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 = ([H2O])^(-1) ([KOH])^(-1) ([Al])^(-2) ([KNO2])^(-1) [NH3] ([KAlO2])^2 = ([NH3] ([KAlO2])^2)/([H2O] [KOH] ([Al])^2 [KNO2])

Construct the rate of reaction expression for: H_2O + KOH + Al + KNO_2 ⟶ NH_3 + KAlO2 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: H_2O + KOH + 2 Al + KNO_2 ⟶ NH_3 + 2 KAlO2 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 H_2O | 1 | -1 KOH | 1 | -1 Al | 2 | -2 KNO_2 | 1 | -1 NH_3 | 1 | 1 KAlO2 | 2 | 2 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) KOH | 1 | -1 | -(Δ[KOH])/(Δt) Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) KNO_2 | 1 | -1 | -(Δ[KNO2])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(Δt) KAlO2 | 2 | 2 | 1/2 (Δ[KAlO2])/(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[H2O])/(Δt) = -(Δ[KOH])/(Δt) = -1/2 (Δ[Al])/(Δt) = -(Δ[KNO2])/(Δt) = (Δ[NH3])/(Δt) = 1/2 (Δ[KAlO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium hydroxide | aluminum | potassium nitrite | ammonia | KAlO2 formula | H_2O | KOH | Al | KNO_2 | NH_3 | KAlO2 Hill formula | H_2O | HKO | Al | KNO_2 | H_3N | AlKO2 name | water | potassium hydroxide | aluminum | potassium nitrite | ammonia |