HNO3 + Al = H2O + NO2 + Al2O3

HNO_3 nitric acid + Al aluminum ⟶ H_2O water + NO_2 nitrogen dioxide + Al_2O_3 aluminum oxide

Balance the chemical equation algebraically: HNO_3 + Al ⟶ H_2O + NO_2 + Al_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Al ⟶ c_3 H_2O + c_4 NO_2 + c_5 Al_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Al: H: | c_1 = 2 c_3 N: | c_1 = c_4 O: | 3 c_1 = c_3 + 2 c_4 + 3 c_5 Al: | c_2 = 2 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 6 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HNO_3 + 2 Al ⟶ 3 H_2O + 6 NO_2 + Al_2O_3

+ ⟶ + +

nitric acid + aluminum ⟶ water + nitrogen dioxide + aluminum oxide

| nitric acid | aluminum | water | nitrogen dioxide | aluminum oxide molecular entropy | 156 J/(mol K) | 28.3 J/(mol K) | 69.91 J/(mol K) | 240 J/(mol K) | 51 J/(mol K) total entropy | 936 J/(mol K) | 56.6 J/(mol K) | 209.7 J/(mol K) | 1440 J/(mol K) | 51 J/(mol K) | S_initial = 992.6 J/(mol K) | | S_final = 1701 J/(mol K) | | ΔS_rxn^0 | 1701 J/(mol K) - 992.6 J/(mol K) = 708.1 J/(mol K) (endoentropic) | | | |

Construct the equilibrium constant, K, expression for: HNO_3 + Al ⟶ H_2O + NO_2 + Al_2O_3 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: 6 HNO_3 + 2 Al ⟶ 3 H_2O + 6 NO_2 + Al_2O_3 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 | 6 | -6 Al | 2 | -2 H_2O | 3 | 3 NO_2 | 6 | 6 Al_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 6 | -6 | ([HNO3])^(-6) Al | 2 | -2 | ([Al])^(-2) H_2O | 3 | 3 | ([H2O])^3 NO_2 | 6 | 6 | ([NO2])^6 Al_2O_3 | 1 | 1 | [Al2O3] 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])^(-6) ([Al])^(-2) ([H2O])^3 ([NO2])^6 [Al2O3] = (([H2O])^3 ([NO2])^6 [Al2O3])/(([HNO3])^6 ([Al])^2)

Construct the rate of reaction expression for: HNO_3 + Al ⟶ H_2O + NO_2 + Al_2O_3 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: 6 HNO_3 + 2 Al ⟶ 3 H_2O + 6 NO_2 + Al_2O_3 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 | 6 | -6 Al | 2 | -2 H_2O | 3 | 3 NO_2 | 6 | 6 Al_2O_3 | 1 | 1 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 | 6 | -6 | -1/6 (Δ[HNO3])/(Δt) Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NO_2 | 6 | 6 | 1/6 (Δ[NO2])/(Δt) Al_2O_3 | 1 | 1 | (Δ[Al2O3])/(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 = -1/6 (Δ[HNO3])/(Δt) = -1/2 (Δ[Al])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/6 (Δ[NO2])/(Δt) = (Δ[Al2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | aluminum | water | nitrogen dioxide | aluminum oxide formula | HNO_3 | Al | H_2O | NO_2 | Al_2O_3 name | nitric acid | aluminum | water | nitrogen dioxide | aluminum oxide IUPAC name | nitric acid | aluminum | water | Nitrogen dioxide | dialuminum;oxygen(2-)