H2O + HNO3 + SO2 = H2SO4 + N2O3

H_2O water + HNO_3 nitric acid + SO_2 sulfur dioxide ⟶ H_2SO_4 sulfuric acid + N_2O_3 nitrogen trioxide

Balance the chemical equation algebraically: H_2O + HNO_3 + SO_2 ⟶ H_2SO_4 + N_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_3 + c_3 SO_2 ⟶ c_4 H_2SO_4 + c_5 N_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N and S: H: | 2 c_1 + c_2 = 2 c_4 O: | c_1 + 3 c_2 + 2 c_3 = 4 c_4 + 3 c_5 N: | c_2 = 2 c_5 S: | c_3 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 2 HNO_3 + 2 SO_2 ⟶ 2 H_2SO_4 + N_2O_3

+ + ⟶ +

water + nitric acid + sulfur dioxide ⟶ sulfuric acid + nitrogen trioxide

| water | nitric acid | sulfur dioxide | sulfuric acid | nitrogen trioxide molecular free energy | -237.1 kJ/mol | -80.7 kJ/mol | -300.1 kJ/mol | -690 kJ/mol | 142.4 kJ/mol total free energy | -237.1 kJ/mol | -161.4 kJ/mol | -600.2 kJ/mol | -1380 kJ/mol | 142.4 kJ/mol | G_initial = -998.7 kJ/mol | | | G_final = -1238 kJ/mol | ΔG_rxn^0 | -1238 kJ/mol - -998.7 kJ/mol = -238.9 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: H_2O + HNO_3 + SO_2 ⟶ H_2SO_4 + N_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: H_2O + 2 HNO_3 + 2 SO_2 ⟶ 2 H_2SO_4 + N_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 H_2O | 1 | -1 HNO_3 | 2 | -2 SO_2 | 2 | -2 H_2SO_4 | 2 | 2 N_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 H_2O | 1 | -1 | ([H2O])^(-1) HNO_3 | 2 | -2 | ([HNO3])^(-2) SO_2 | 2 | -2 | ([SO2])^(-2) H_2SO_4 | 2 | 2 | ([H2SO4])^2 N_2O_3 | 1 | 1 | [N2O3] 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 = ([H2O])^(-1) ([HNO3])^(-2) ([SO2])^(-2) ([H2SO4])^2 [N2O3] = (([H2SO4])^2 [N2O3])/([H2O] ([HNO3])^2 ([SO2])^2)

Construct the rate of reaction expression for: H_2O + HNO_3 + SO_2 ⟶ H_2SO_4 + N_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: H_2O + 2 HNO_3 + 2 SO_2 ⟶ 2 H_2SO_4 + N_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 H_2O | 1 | -1 HNO_3 | 2 | -2 SO_2 | 2 | -2 H_2SO_4 | 2 | 2 N_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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) SO_2 | 2 | -2 | -1/2 (Δ[SO2])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) N_2O_3 | 1 | 1 | (Δ[N2O3])/(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 = -(Δ[H2O])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/2 (Δ[SO2])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = (Δ[N2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitric acid | sulfur dioxide | sulfuric acid | nitrogen trioxide formula | H_2O | HNO_3 | SO_2 | H_2SO_4 | N_2O_3 Hill formula | H_2O | HNO_3 | O_2S | H_2O_4S | N_2O_3 name | water | nitric acid | sulfur dioxide | sulfuric acid | nitrogen trioxide IUPAC name | water | nitric acid | sulfur dioxide | sulfuric acid | nitramide