HCl + HNO3 = H2O + Cl2 + NO2

HCl hydrogen chloride + HNO_3 nitric acid ⟶ H_2O water + Cl_2 chlorine + NO_2 nitrogen dioxide

Balance the chemical equation algebraically: HCl + HNO_3 ⟶ H_2O + Cl_2 + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HNO_3 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N and O: Cl: | c_1 = 2 c_4 H: | c_1 + c_2 = 2 c_3 N: | c_2 = c_5 O: | 3 c_2 = c_3 + 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + 2 HNO_3 ⟶ 2 H_2O + Cl_2 + 2 NO_2

+ ⟶ + +

hydrogen chloride + nitric acid ⟶ water + chlorine + nitrogen dioxide

| hydrogen chloride | nitric acid | water | chlorine | nitrogen dioxide molecular free energy | -95.3 kJ/mol | -80.7 kJ/mol | -237.1 kJ/mol | 0 kJ/mol | 51.3 kJ/mol total free energy | -190.6 kJ/mol | -161.4 kJ/mol | -474.2 kJ/mol | 0 kJ/mol | 102.6 kJ/mol | G_initial = -352 kJ/mol | | G_final = -371.6 kJ/mol | | ΔG_rxn^0 | -371.6 kJ/mol - -352 kJ/mol = -19.6 kJ/mol (exergonic) | | | |

| hydrogen chloride | nitric acid | water | chlorine | nitrogen dioxide molecular entropy | 187 J/(mol K) | 156 J/(mol K) | 69.91 J/(mol K) | 223 J/(mol K) | 240 J/(mol K) total entropy | 374 J/(mol K) | 312 J/(mol K) | 139.8 J/(mol K) | 223 J/(mol K) | 480 J/(mol K) | S_initial = 686 J/(mol K) | | S_final = 842.8 J/(mol K) | | ΔS_rxn^0 | 842.8 J/(mol K) - 686 J/(mol K) = 156.8 J/(mol K) (endoentropic) | | | |

Construct the equilibrium constant, K, expression for: HCl + HNO_3 ⟶ H_2O + Cl_2 + 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 HCl + 2 HNO_3 ⟶ 2 H_2O + Cl_2 + 2 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 HCl | 2 | -2 HNO_3 | 2 | -2 H_2O | 2 | 2 Cl_2 | 1 | 1 NO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 2 | -2 | ([HCl])^(-2) HNO_3 | 2 | -2 | ([HNO3])^(-2) H_2O | 2 | 2 | ([H2O])^2 Cl_2 | 1 | 1 | [Cl2] NO_2 | 2 | 2 | ([NO2])^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 = ([HCl])^(-2) ([HNO3])^(-2) ([H2O])^2 [Cl2] ([NO2])^2 = (([H2O])^2 [Cl2] ([NO2])^2)/(([HCl])^2 ([HNO3])^2)

Construct the rate of reaction expression for: HCl + HNO_3 ⟶ H_2O + Cl_2 + 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 HCl + 2 HNO_3 ⟶ 2 H_2O + Cl_2 + 2 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 HCl | 2 | -2 HNO_3 | 2 | -2 H_2O | 2 | 2 Cl_2 | 1 | 1 NO_2 | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) NO_2 | 2 | 2 | 1/2 (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[HCl])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[Cl2])/(Δt) = 1/2 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | nitric acid | water | chlorine | nitrogen dioxide formula | HCl | HNO_3 | H_2O | Cl_2 | NO_2 Hill formula | ClH | HNO_3 | H_2O | Cl_2 | NO_2 name | hydrogen chloride | nitric acid | water | chlorine | nitrogen dioxide IUPAC name | hydrogen chloride | nitric acid | water | molecular chlorine | Nitrogen dioxide