KOH + Al + KNO3 = H2O + NH3 + K3AlO3

KOH potassium hydroxide + Al aluminum + KNO_3 potassium nitrate ⟶ H_2O water + NH_3 ammonia + K3AlO3

Balance the chemical equation algebraically: KOH + Al + KNO_3 ⟶ H_2O + NH_3 + K3AlO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Al + c_3 KNO_3 ⟶ c_4 H_2O + c_5 NH_3 + c_6 K3AlO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Al and N: H: | c_1 = 2 c_4 + 3 c_5 K: | c_1 + c_3 = 3 c_6 O: | c_1 + 3 c_3 = c_4 + 3 c_6 Al: | 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 = 7 c_2 = 8/3 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 8/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 21 c_2 = 8 c_3 = 3 c_4 = 6 c_5 = 3 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 21 KOH + 8 Al + 3 KNO_3 ⟶ 6 H_2O + 3 NH_3 + 8 K3AlO3

+ + ⟶ + + K3AlO3

potassium hydroxide + aluminum + potassium nitrate ⟶ water + ammonia + K3AlO3

Construct the equilibrium constant, K, expression for: KOH + Al + KNO_3 ⟶ H_2O + NH_3 + K3AlO3 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: 21 KOH + 8 Al + 3 KNO_3 ⟶ 6 H_2O + 3 NH_3 + 8 K3AlO3 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 | 21 | -21 Al | 8 | -8 KNO_3 | 3 | -3 H_2O | 6 | 6 NH_3 | 3 | 3 K3AlO3 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 21 | -21 | ([KOH])^(-21) Al | 8 | -8 | ([Al])^(-8) KNO_3 | 3 | -3 | ([KNO3])^(-3) H_2O | 6 | 6 | ([H2O])^6 NH_3 | 3 | 3 | ([NH3])^3 K3AlO3 | 8 | 8 | ([K3AlO3])^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])^(-21) ([Al])^(-8) ([KNO3])^(-3) ([H2O])^6 ([NH3])^3 ([K3AlO3])^8 = (([H2O])^6 ([NH3])^3 ([K3AlO3])^8)/(([KOH])^21 ([Al])^8 ([KNO3])^3)

Construct the rate of reaction expression for: KOH + Al + KNO_3 ⟶ H_2O + NH_3 + K3AlO3 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: 21 KOH + 8 Al + 3 KNO_3 ⟶ 6 H_2O + 3 NH_3 + 8 K3AlO3 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 | 21 | -21 Al | 8 | -8 KNO_3 | 3 | -3 H_2O | 6 | 6 NH_3 | 3 | 3 K3AlO3 | 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 | 21 | -21 | -1/21 (Δ[KOH])/(Δt) Al | 8 | -8 | -1/8 (Δ[Al])/(Δt) KNO_3 | 3 | -3 | -1/3 (Δ[KNO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) NH_3 | 3 | 3 | 1/3 (Δ[NH3])/(Δt) K3AlO3 | 8 | 8 | 1/8 (Δ[K3AlO3])/(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 = -1/21 (Δ[KOH])/(Δt) = -1/8 (Δ[Al])/(Δt) = -1/3 (Δ[KNO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[NH3])/(Δt) = 1/8 (Δ[K3AlO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | aluminum | potassium nitrate | water | ammonia | K3AlO3 formula | KOH | Al | KNO_3 | H_2O | NH_3 | K3AlO3 Hill formula | HKO | Al | KNO_3 | H_2O | H_3N | AlK3O3 name | potassium hydroxide | aluminum | potassium nitrate | water | ammonia |