NO + Ba(OH)2 = H2O + N2 + Ba(NO2)2

NO nitric oxide + Ba(OH)_2 barium hydroxide ⟶ H_2O water + N_2 nitrogen + BaN_2O_4 barium nitrite

Balance the chemical equation algebraically: NO + Ba(OH)_2 ⟶ H_2O + N_2 + BaN_2O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NO + c_2 Ba(OH)_2 ⟶ c_3 H_2O + c_4 N_2 + c_5 BaN_2O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O, Ba and H: N: | c_1 = 2 c_4 + 2 c_5 O: | c_1 + 2 c_2 = c_3 + 4 c_5 Ba: | c_2 = c_5 H: | 2 c_2 = 2 c_3 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 = 6 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: | | 6 NO + 2 Ba(OH)_2 ⟶ 2 H_2O + N_2 + 2 BaN_2O_4

+ ⟶ + +

nitric oxide + barium hydroxide ⟶ water + nitrogen + barium nitrite

| nitric oxide | barium hydroxide | water | nitrogen | barium nitrite molecular enthalpy | 91.3 kJ/mol | -944.7 kJ/mol | -285.8 kJ/mol | 0 kJ/mol | -768.2 kJ/mol total enthalpy | 547.8 kJ/mol | -1889 kJ/mol | -571.7 kJ/mol | 0 kJ/mol | -1536 kJ/mol | H_initial = -1342 kJ/mol | | H_final = -2108 kJ/mol | | ΔH_rxn^0 | -2108 kJ/mol - -1342 kJ/mol = -766.5 kJ/mol (exothermic) | | | |

Construct the equilibrium constant, K, expression for: NO + Ba(OH)_2 ⟶ H_2O + N_2 + BaN_2O_4 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 NO + 2 Ba(OH)_2 ⟶ 2 H_2O + N_2 + 2 BaN_2O_4 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 NO | 6 | -6 Ba(OH)_2 | 2 | -2 H_2O | 2 | 2 N_2 | 1 | 1 BaN_2O_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NO | 6 | -6 | ([NO])^(-6) Ba(OH)_2 | 2 | -2 | ([Ba(OH)2])^(-2) H_2O | 2 | 2 | ([H2O])^2 N_2 | 1 | 1 | [N2] BaN_2O_4 | 2 | 2 | ([BaN2O4])^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 = ([NO])^(-6) ([Ba(OH)2])^(-2) ([H2O])^2 [N2] ([BaN2O4])^2 = (([H2O])^2 [N2] ([BaN2O4])^2)/(([NO])^6 ([Ba(OH)2])^2)

Construct the rate of reaction expression for: NO + Ba(OH)_2 ⟶ H_2O + N_2 + BaN_2O_4 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 NO + 2 Ba(OH)_2 ⟶ 2 H_2O + N_2 + 2 BaN_2O_4 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 NO | 6 | -6 Ba(OH)_2 | 2 | -2 H_2O | 2 | 2 N_2 | 1 | 1 BaN_2O_4 | 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 NO | 6 | -6 | -1/6 (Δ[NO])/(Δt) Ba(OH)_2 | 2 | -2 | -1/2 (Δ[Ba(OH)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) BaN_2O_4 | 2 | 2 | 1/2 (Δ[BaN2O4])/(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[NO])/(Δt) = -1/2 (Δ[Ba(OH)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[N2])/(Δt) = 1/2 (Δ[BaN2O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric oxide | barium hydroxide | water | nitrogen | barium nitrite formula | NO | Ba(OH)_2 | H_2O | N_2 | BaN_2O_4 Hill formula | NO | BaH_2O_2 | H_2O | N_2 | BaN_2O_4 name | nitric oxide | barium hydroxide | water | nitrogen | barium nitrite IUPAC name | nitric oxide | barium(+2) cation dihydroxide | water | molecular nitrogen | barium(+2) cation dinitrite

| nitric oxide | barium hydroxide | water | nitrogen | barium nitrite molar mass | 30.006 g/mol | 171.34 g/mol | 18.015 g/mol | 28.014 g/mol | 229.34 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -163.6 °C | 300 °C | 0 °C | -210 °C | 269 °C boiling point | -151.7 °C | | 99.9839 °C | -195.79 °C | density | 0.001226 g/cm^3 (at 25 °C) | 2.2 g/cm^3 | 1 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | 3.23 g/cm^3 solubility in water | | | | insoluble | surface tension | | | 0.0728 N/m | 0.0066 N/m | dynamic viscosity | 1.911×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |