NaOH + N2O5 = Na2O + N(OH)5

NaOH sodium hydroxide + N_2O_5 dinitrogen pentoxide ⟶ Na_2O sodium oxide + N(OH)5

Balance the chemical equation algebraically: NaOH + N_2O_5 ⟶ Na_2O + N(OH)5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 N_2O_5 ⟶ c_3 Na_2O + c_4 N(OH)5 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 = 5 c_4 Na: | c_1 = 2 c_3 O: | c_1 + 5 c_2 = c_3 + 5 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 = 10 c_2 = 1 c_3 = 5 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 NaOH + N_2O_5 ⟶ 5 Na_2O + 2 N(OH)5

+ ⟶ + N(OH)5

sodium hydroxide + dinitrogen pentoxide ⟶ sodium oxide + N(OH)5

Construct the equilibrium constant, K, expression for: NaOH + N_2O_5 ⟶ Na_2O + N(OH)5 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: 10 NaOH + N_2O_5 ⟶ 5 Na_2O + 2 N(OH)5 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 | 10 | -10 N_2O_5 | 1 | -1 Na_2O | 5 | 5 N(OH)5 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 10 | -10 | ([NaOH])^(-10) N_2O_5 | 1 | -1 | ([N2O5])^(-1) Na_2O | 5 | 5 | ([Na2O])^5 N(OH)5 | 2 | 2 | ([N(OH)5])^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])^(-10) ([N2O5])^(-1) ([Na2O])^5 ([N(OH)5])^2 = (([Na2O])^5 ([N(OH)5])^2)/(([NaOH])^10 [N2O5])

Construct the rate of reaction expression for: NaOH + N_2O_5 ⟶ Na_2O + N(OH)5 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: 10 NaOH + N_2O_5 ⟶ 5 Na_2O + 2 N(OH)5 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 | 10 | -10 N_2O_5 | 1 | -1 Na_2O | 5 | 5 N(OH)5 | 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 | 10 | -10 | -1/10 (Δ[NaOH])/(Δt) N_2O_5 | 1 | -1 | -(Δ[N2O5])/(Δt) Na_2O | 5 | 5 | 1/5 (Δ[Na2O])/(Δt) N(OH)5 | 2 | 2 | 1/2 (Δ[N(OH)5])/(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 = -1/10 (Δ[NaOH])/(Δt) = -(Δ[N2O5])/(Δt) = 1/5 (Δ[Na2O])/(Δt) = 1/2 (Δ[N(OH)5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | dinitrogen pentoxide | sodium oxide | N(OH)5 formula | NaOH | N_2O_5 | Na_2O | N(OH)5 Hill formula | HNaO | N_2O_5 | Na_2O | H5NO5 name | sodium hydroxide | dinitrogen pentoxide | sodium oxide | IUPAC name | sodium hydroxide | nitro nitrate | disodium oxygen(-2) anion |

| sodium hydroxide | dinitrogen pentoxide | sodium oxide | N(OH)5 molar mass | 39.997 g/mol | 108.01 g/mol | 61.979 g/mol | 99.04 g/mol phase | solid (at STP) | solid (at STP) | | melting point | 323 °C | 30 °C | | boiling point | 1390 °C | 47 °C | | density | 2.13 g/cm^3 | 2.05 g/cm^3 | 2.27 g/cm^3 | solubility in water | soluble | | | surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | |