NH3 + O3 = H2O + NO2

NH_3 ammonia + O_3 ozone ⟶ H_2O water + NO_2 nitrogen dioxide

Balance the chemical equation algebraically: NH_3 + O_3 ⟶ H_2O + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 O_3 ⟶ 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: | 3 c_1 = 2 c_3 N: | c_1 = c_4 O: | 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 7/6 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 6, to eliminate fractional coefficients: c_1 = 6 c_2 = 7 c_3 = 9 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NH_3 + 7 O_3 ⟶ 9 H_2O + 6 NO_2

+ ⟶ +

ammonia + ozone ⟶ water + nitrogen dioxide

| ammonia | ozone | water | nitrogen dioxide molecular enthalpy | -45.9 kJ/mol | 142.7 kJ/mol | -285.8 kJ/mol | 33.2 kJ/mol total enthalpy | -275.4 kJ/mol | 998.9 kJ/mol | -2572 kJ/mol | 199.2 kJ/mol | H_initial = 723.5 kJ/mol | | H_final = -2373 kJ/mol | ΔH_rxn^0 | -2373 kJ/mol - 723.5 kJ/mol = -3097 kJ/mol (exothermic) | | |

| ammonia | ozone | water | nitrogen dioxide molecular free energy | -16.4 kJ/mol | 163.2 kJ/mol | -237.1 kJ/mol | 51.3 kJ/mol total free energy | -98.4 kJ/mol | 1142 kJ/mol | -2134 kJ/mol | 307.8 kJ/mol | G_initial = 1044 kJ/mol | | G_final = -1826 kJ/mol | ΔG_rxn^0 | -1826 kJ/mol - 1044 kJ/mol = -2870 kJ/mol (exergonic) | | |

| ammonia | ozone | water | nitrogen dioxide molecular entropy | 193 J/(mol K) | 239 J/(mol K) | 69.91 J/(mol K) | 240 J/(mol K) total entropy | 1158 J/(mol K) | 1673 J/(mol K) | 629.2 J/(mol K) | 1440 J/(mol K) | S_initial = 2831 J/(mol K) | | S_final = 2069 J/(mol K) | ΔS_rxn^0 | 2069 J/(mol K) - 2831 J/(mol K) = -761.8 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: NH_3 + O_3 ⟶ 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: 6 NH_3 + 7 O_3 ⟶ 9 H_2O + 6 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 NH_3 | 6 | -6 O_3 | 7 | -7 H_2O | 9 | 9 NO_2 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 6 | -6 | ([NH3])^(-6) O_3 | 7 | -7 | ([O3])^(-7) H_2O | 9 | 9 | ([H2O])^9 NO_2 | 6 | 6 | ([NO2])^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 = ([NH3])^(-6) ([O3])^(-7) ([H2O])^9 ([NO2])^6 = (([H2O])^9 ([NO2])^6)/(([NH3])^6 ([O3])^7)

Construct the rate of reaction expression for: NH_3 + O_3 ⟶ 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: 6 NH_3 + 7 O_3 ⟶ 9 H_2O + 6 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 NH_3 | 6 | -6 O_3 | 7 | -7 H_2O | 9 | 9 NO_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 NH_3 | 6 | -6 | -1/6 (Δ[NH3])/(Δt) O_3 | 7 | -7 | -1/7 (Δ[O3])/(Δt) H_2O | 9 | 9 | 1/9 (Δ[H2O])/(Δt) NO_2 | 6 | 6 | 1/6 (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 = -1/6 (Δ[NH3])/(Δt) = -1/7 (Δ[O3])/(Δt) = 1/9 (Δ[H2O])/(Δt) = 1/6 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | ozone | water | nitrogen dioxide formula | NH_3 | O_3 | H_2O | NO_2 Hill formula | H_3N | O_3 | H_2O | NO_2 name | ammonia | ozone | water | nitrogen dioxide IUPAC name | ammonia | ozone | water | Nitrogen dioxide

| ammonia | ozone | water | nitrogen dioxide molar mass | 17.031 g/mol | 47.997 g/mol | 18.015 g/mol | 46.005 g/mol phase | gas (at STP) | gas (at STP) | liquid (at STP) | gas (at STP) melting point | -77.73 °C | -192.2 °C | 0 °C | -11 °C boiling point | -33.33 °C | -111.9 °C | 99.9839 °C | 21 °C density | 6.96×10^-4 g/cm^3 (at 25 °C) | 0.001962 g/cm^3 (at 25 °C) | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) solubility in water | | | | reacts surface tension | 0.0234 N/m | | 0.0728 N/m | dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) odor | | | odorless |