HNO3 + NO = H2O + NO2

HNO_3 nitric acid + NO nitric oxide ⟶ H_2O water + NO_2 nitrogen dioxide

Balance the chemical equation algebraically: HNO_3 + NO ⟶ H_2O + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 NO ⟶ c_3 H_2O + c_4 NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N and O: H: | c_1 = 2 c_3 N: | c_1 + c_2 = c_4 O: | 3 c_1 + c_2 = c_3 + 2 c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + NO ⟶ H_2O + 3 NO_2

+ ⟶ +

nitric acid + nitric oxide ⟶ water + nitrogen dioxide

| nitric acid | nitric oxide | water | nitrogen dioxide molecular free energy | -80.7 kJ/mol | 87.6 kJ/mol | -237.1 kJ/mol | 51.3 kJ/mol total free energy | -161.4 kJ/mol | 87.6 kJ/mol | -237.1 kJ/mol | 153.9 kJ/mol | G_initial = -73.8 kJ/mol | | G_final = -83.2 kJ/mol | ΔG_rxn^0 | -83.2 kJ/mol - -73.8 kJ/mol = -9.4 kJ/mol (exergonic) | | |

| nitric acid | nitric oxide | water | nitrogen dioxide molecular entropy | 156 J/(mol K) | 211 J/(mol K) | 69.91 J/(mol K) | 240 J/(mol K) total entropy | 312 J/(mol K) | 211 J/(mol K) | 69.91 J/(mol K) | 720 J/(mol K) | S_initial = 523 J/(mol K) | | S_final = 789.9 J/(mol K) | ΔS_rxn^0 | 789.9 J/(mol K) - 523 J/(mol K) = 266.9 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: HNO_3 + NO ⟶ H_2O + NO_2 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: 2 HNO_3 + NO ⟶ H_2O + 3 NO_2 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 | 2 | -2 NO | 1 | -1 H_2O | 1 | 1 NO_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) NO | 1 | -1 | ([NO])^(-1) H_2O | 1 | 1 | [H2O] NO_2 | 3 | 3 | ([NO2])^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 = ([HNO3])^(-2) ([NO])^(-1) [H2O] ([NO2])^3 = ([H2O] ([NO2])^3)/(([HNO3])^2 [NO])

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

| nitric acid | nitric oxide | water | nitrogen dioxide formula | HNO_3 | NO | H_2O | NO_2 name | nitric acid | nitric oxide | water | nitrogen dioxide IUPAC name | nitric acid | nitric oxide | water | Nitrogen dioxide