NaOH + N2O3 = H2O + NaNO2

NaOH sodium hydroxide + N_2O_3 nitrogen trioxide ⟶ H_2O water + NaNO_2 sodium nitrite

Balance the chemical equation algebraically: NaOH + N_2O_3 ⟶ H_2O + NaNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 N_2O_3 ⟶ c_3 H_2O + c_4 NaNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O and N: H: | c_1 = 2 c_3 Na: | c_1 = c_4 O: | c_1 + 3 c_2 = c_3 + 2 c_4 N: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + N_2O_3 ⟶ H_2O + 2 NaNO_2

+ ⟶ +

sodium hydroxide + nitrogen trioxide ⟶ water + sodium nitrite

| sodium hydroxide | nitrogen trioxide | water | sodium nitrite molecular enthalpy | -425.8 kJ/mol | 86.6 kJ/mol | -285.8 kJ/mol | -359 kJ/mol total enthalpy | -851.6 kJ/mol | 86.6 kJ/mol | -285.8 kJ/mol | -718 kJ/mol | H_initial = -765 kJ/mol | | H_final = -1004 kJ/mol | ΔH_rxn^0 | -1004 kJ/mol - -765 kJ/mol = -238.8 kJ/mol (exothermic) | | |

| sodium hydroxide | nitrogen trioxide | water | sodium nitrite molecular free energy | -379.7 kJ/mol | 142.4 kJ/mol | -237.1 kJ/mol | -284.6 kJ/mol total free energy | -759.4 kJ/mol | 142.4 kJ/mol | -237.1 kJ/mol | -569.2 kJ/mol | G_initial = -617 kJ/mol | | G_final = -806.3 kJ/mol | ΔG_rxn^0 | -806.3 kJ/mol - -617 kJ/mol = -189.3 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: NaOH + N_2O_3 ⟶ H_2O + NaNO_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 NaOH + N_2O_3 ⟶ H_2O + 2 NaNO_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 NaOH | 2 | -2 N_2O_3 | 1 | -1 H_2O | 1 | 1 NaNO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) N_2O_3 | 1 | -1 | ([N2O3])^(-1) H_2O | 1 | 1 | [H2O] NaNO_2 | 2 | 2 | ([NaNO2])^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 = ([NaOH])^(-2) ([N2O3])^(-1) [H2O] ([NaNO2])^2 = ([H2O] ([NaNO2])^2)/(([NaOH])^2 [N2O3])

Construct the rate of reaction expression for: NaOH + N_2O_3 ⟶ H_2O + NaNO_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 NaOH + N_2O_3 ⟶ H_2O + 2 NaNO_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 NaOH | 2 | -2 N_2O_3 | 1 | -1 H_2O | 1 | 1 NaNO_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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) N_2O_3 | 1 | -1 | -(Δ[N2O3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NaNO_2 | 2 | 2 | 1/2 (Δ[NaNO2])/(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[NaOH])/(Δt) = -(Δ[N2O3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[NaNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | nitrogen trioxide | water | sodium nitrite formula | NaOH | N_2O_3 | H_2O | NaNO_2 Hill formula | HNaO | N_2O_3 | H_2O | NNaO_2 name | sodium hydroxide | nitrogen trioxide | water | sodium nitrite IUPAC name | sodium hydroxide | nitramide | water | sodium nitrite

| sodium hydroxide | nitrogen trioxide | water | sodium nitrite molar mass | 39.997 g/mol | 76.011 g/mol | 18.015 g/mol | 68.995 g/mol phase | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) melting point | 323 °C | -111 °C | 0 °C | 271 °C boiling point | 1390 °C | -27 °C | 99.9839 °C | density | 2.13 g/cm^3 | 1.4 g/cm^3 (at 2 °C) | 1 g/cm^3 | 2.168 g/cm^3 solubility in water | soluble | very soluble | | surface tension | 0.07435 N/m | | 0.0728 N/m | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |