HNO3 + KOH + Al = H2O + KNO2 + KAlO2

HNO_3 nitric acid + KOH potassium hydroxide + Al aluminum ⟶ H_2O water + KNO_2 potassium nitrite + KAlO2

Balance the chemical equation algebraically: HNO_3 + KOH + Al ⟶ H_2O + KNO_2 + KAlO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 KOH + c_3 Al ⟶ c_4 H_2O + c_5 KNO_2 + c_6 KAlO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, K and Al: H: | c_1 + c_2 = 2 c_4 N: | c_1 = c_5 O: | 3 c_1 + c_2 = c_4 + 2 c_5 + 2 c_6 K: | c_2 = c_5 + c_6 Al: | c_3 = c_6 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 = 3/2 c_2 = 5/2 c_3 = 1 c_4 = 2 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 5 c_3 = 2 c_4 = 4 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 HNO_3 + 5 KOH + 2 Al ⟶ 4 H_2O + 3 KNO_2 + 2 KAlO2

+ + ⟶ + + KAlO2

nitric acid + potassium hydroxide + aluminum ⟶ water + potassium nitrite + KAlO2

Construct the equilibrium constant, K, expression for: HNO_3 + KOH + Al ⟶ H_2O + KNO_2 + 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: 3 HNO_3 + 5 KOH + 2 Al ⟶ 4 H_2O + 3 KNO_2 + 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 HNO_3 | 3 | -3 KOH | 5 | -5 Al | 2 | -2 H_2O | 4 | 4 KNO_2 | 3 | 3 KAlO2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 3 | -3 | ([HNO3])^(-3) KOH | 5 | -5 | ([KOH])^(-5) Al | 2 | -2 | ([Al])^(-2) H_2O | 4 | 4 | ([H2O])^4 KNO_2 | 3 | 3 | ([KNO2])^3 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 = ([HNO3])^(-3) ([KOH])^(-5) ([Al])^(-2) ([H2O])^4 ([KNO2])^3 ([KAlO2])^2 = (([H2O])^4 ([KNO2])^3 ([KAlO2])^2)/(([HNO3])^3 ([KOH])^5 ([Al])^2)

Construct the rate of reaction expression for: HNO_3 + KOH + Al ⟶ H_2O + KNO_2 + 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: 3 HNO_3 + 5 KOH + 2 Al ⟶ 4 H_2O + 3 KNO_2 + 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 HNO_3 | 3 | -3 KOH | 5 | -5 Al | 2 | -2 H_2O | 4 | 4 KNO_2 | 3 | 3 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 HNO_3 | 3 | -3 | -1/3 (Δ[HNO3])/(Δt) KOH | 5 | -5 | -1/5 (Δ[KOH])/(Δt) Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KNO_2 | 3 | 3 | 1/3 (Δ[KNO2])/(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 = -1/3 (Δ[HNO3])/(Δt) = -1/5 (Δ[KOH])/(Δt) = -1/2 (Δ[Al])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[KNO2])/(Δt) = 1/2 (Δ[KAlO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | potassium hydroxide | aluminum | water | potassium nitrite | KAlO2 formula | HNO_3 | KOH | Al | H_2O | KNO_2 | KAlO2 Hill formula | HNO_3 | HKO | Al | H_2O | KNO_2 | AlKO2 name | nitric acid | potassium hydroxide | aluminum | water | potassium nitrite |