Ba(OH)2 + N2O5 = H2O + Ba(NO3)2

Ba(OH)_2 barium hydroxide + N_2O_5 dinitrogen pentoxide ⟶ H_2O water + Ba(NO_3)_2 barium nitrate

Balance the chemical equation algebraically: Ba(OH)_2 + N_2O_5 ⟶ H_2O + Ba(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ba(OH)_2 + c_2 N_2O_5 ⟶ c_3 H_2O + c_4 Ba(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ba, H, O and N: Ba: | c_1 = c_4 H: | 2 c_1 = 2 c_3 O: | 2 c_1 + 5 c_2 = c_3 + 6 c_4 N: | 2 c_2 = 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Ba(OH)_2 + N_2O_5 ⟶ H_2O + Ba(NO_3)_2

+ ⟶ +

barium hydroxide + dinitrogen pentoxide ⟶ water + barium nitrate

| barium hydroxide | dinitrogen pentoxide | water | barium nitrate molecular enthalpy | -944.7 kJ/mol | -43.1 kJ/mol | -285.8 kJ/mol | -988 kJ/mol total enthalpy | -944.7 kJ/mol | -43.1 kJ/mol | -285.8 kJ/mol | -988 kJ/mol | H_initial = -987.8 kJ/mol | | H_final = -1274 kJ/mol | ΔH_rxn^0 | -1274 kJ/mol - -987.8 kJ/mol = -286 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Ba(OH)_2 + N_2O_5 ⟶ H_2O + Ba(NO_3)_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: Ba(OH)_2 + N_2O_5 ⟶ H_2O + Ba(NO_3)_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 Ba(OH)_2 | 1 | -1 N_2O_5 | 1 | -1 H_2O | 1 | 1 Ba(NO_3)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ba(OH)_2 | 1 | -1 | ([Ba(OH)2])^(-1) N_2O_5 | 1 | -1 | ([N2O5])^(-1) H_2O | 1 | 1 | [H2O] Ba(NO_3)_2 | 1 | 1 | [Ba(NO3)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 = ([Ba(OH)2])^(-1) ([N2O5])^(-1) [H2O] [Ba(NO3)2] = ([H2O] [Ba(NO3)2])/([Ba(OH)2] [N2O5])

Construct the rate of reaction expression for: Ba(OH)_2 + N_2O_5 ⟶ H_2O + Ba(NO_3)_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: Ba(OH)_2 + N_2O_5 ⟶ H_2O + Ba(NO_3)_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 Ba(OH)_2 | 1 | -1 N_2O_5 | 1 | -1 H_2O | 1 | 1 Ba(NO_3)_2 | 1 | 1 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 Ba(OH)_2 | 1 | -1 | -(Δ[Ba(OH)2])/(Δt) N_2O_5 | 1 | -1 | -(Δ[N2O5])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Ba(NO_3)_2 | 1 | 1 | (Δ[Ba(NO3)2])/(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 = -(Δ[Ba(OH)2])/(Δt) = -(Δ[N2O5])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Ba(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| barium hydroxide | dinitrogen pentoxide | water | barium nitrate formula | Ba(OH)_2 | N_2O_5 | H_2O | Ba(NO_3)_2 Hill formula | BaH_2O_2 | N_2O_5 | H_2O | BaN_2O_6 name | barium hydroxide | dinitrogen pentoxide | water | barium nitrate IUPAC name | barium(+2) cation dihydroxide | nitro nitrate | water | barium(+2) cation dinitrate

| barium hydroxide | dinitrogen pentoxide | water | barium nitrate molar mass | 171.34 g/mol | 108.01 g/mol | 18.015 g/mol | 261.34 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | 300 °C | 30 °C | 0 °C | 592 °C boiling point | | 47 °C | 99.9839 °C | density | 2.2 g/cm^3 | 2.05 g/cm^3 | 1 g/cm^3 | 3.23 g/cm^3 surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |