H2O + NO2 + O3 = HNO3 + HNO2

H_2O water + NO_2 nitrogen dioxide + O_3 ozone ⟶ HNO_3 nitric acid + HNO_2 nitrous acid

Balance the chemical equation algebraically: H_2O + NO_2 + O_3 ⟶ HNO_3 + HNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NO_2 + c_3 O_3 ⟶ c_4 HNO_3 + c_5 HNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and N: H: | 2 c_1 = c_4 + c_5 O: | c_1 + 2 c_2 + 3 c_3 = 3 c_4 + 2 c_5 N: | c_2 = c_4 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = 2 c_1 c_3 = 1 c_4 = c_1 + 3 c_5 = c_1 - 3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 9 and solve for the remaining coefficients: c_1 = 9 c_2 = 18 c_3 = 1 c_4 = 12 c_5 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 H_2O + 18 NO_2 + O_3 ⟶ 12 HNO_3 + 6 HNO_2

+ + ⟶ +

water + nitrogen dioxide + ozone ⟶ nitric acid + nitrous acid

Construct the equilibrium constant, K, expression for: H_2O + NO_2 + O_3 ⟶ HNO_3 + HNO_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: 9 H_2O + 18 NO_2 + O_3 ⟶ 12 HNO_3 + 6 HNO_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 H_2O | 9 | -9 NO_2 | 18 | -18 O_3 | 1 | -1 HNO_3 | 12 | 12 HNO_2 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 9 | -9 | ([H2O])^(-9) NO_2 | 18 | -18 | ([NO2])^(-18) O_3 | 1 | -1 | ([O3])^(-1) HNO_3 | 12 | 12 | ([HNO3])^12 HNO_2 | 6 | 6 | ([HNO2])^6 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])^(-9) ([NO2])^(-18) ([O3])^(-1) ([HNO3])^12 ([HNO2])^6 = (([HNO3])^12 ([HNO2])^6)/(([H2O])^9 ([NO2])^18 [O3])

Construct the rate of reaction expression for: H_2O + NO_2 + O_3 ⟶ HNO_3 + HNO_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: 9 H_2O + 18 NO_2 + O_3 ⟶ 12 HNO_3 + 6 HNO_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 H_2O | 9 | -9 NO_2 | 18 | -18 O_3 | 1 | -1 HNO_3 | 12 | 12 HNO_2 | 6 | 6 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 | 9 | -9 | -1/9 (Δ[H2O])/(Δt) NO_2 | 18 | -18 | -1/18 (Δ[NO2])/(Δt) O_3 | 1 | -1 | -(Δ[O3])/(Δt) HNO_3 | 12 | 12 | 1/12 (Δ[HNO3])/(Δt) HNO_2 | 6 | 6 | 1/6 (Δ[HNO2])/(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 = -1/9 (Δ[H2O])/(Δt) = -1/18 (Δ[NO2])/(Δt) = -(Δ[O3])/(Δt) = 1/12 (Δ[HNO3])/(Δt) = 1/6 (Δ[HNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitrogen dioxide | ozone | nitric acid | nitrous acid formula | H_2O | NO_2 | O_3 | HNO_3 | HNO_2 name | water | nitrogen dioxide | ozone | nitric acid | nitrous acid IUPAC name | water | Nitrogen dioxide | ozone | nitric acid | nitrous acid

| water | nitrogen dioxide | ozone | nitric acid | nitrous acid molar mass | 18.015 g/mol | 46.005 g/mol | 47.997 g/mol | 63.012 g/mol | 47.013 g/mol phase | liquid (at STP) | gas (at STP) | gas (at STP) | liquid (at STP) | melting point | 0 °C | -11 °C | -192.2 °C | -41.6 °C | boiling point | 99.9839 °C | 21 °C | -111.9 °C | 83 °C | density | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 0.001962 g/cm^3 (at 25 °C) | 1.5129 g/cm^3 | solubility in water | | reacts | | miscible | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | | 7.6×10^-4 Pa s (at 25 °C) | odor | odorless | | | |