H2O + N2 = H2O2 + N2H4

H_2O water + N_2 nitrogen ⟶ H_2O_2 hydrogen peroxide + NH_2NH_2 diazane

Balance the chemical equation algebraically: H_2O + N_2 ⟶ H_2O_2 + NH_2NH_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 N_2 ⟶ c_3 H_2O_2 + c_4 NH_2NH_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and N: H: | 2 c_1 = 2 c_3 + 4 c_4 O: | c_1 = 2 c_3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + N_2 ⟶ 2 H_2O_2 + NH_2NH_2

+ ⟶ +

water + nitrogen ⟶ hydrogen peroxide + diazane

| water | nitrogen | hydrogen peroxide | diazane molecular free energy | -237.1 kJ/mol | 0 kJ/mol | -120.4 kJ/mol | 149.3 kJ/mol total free energy | -948.4 kJ/mol | 0 kJ/mol | -240.8 kJ/mol | 149.3 kJ/mol | G_initial = -948.4 kJ/mol | | G_final = -91.5 kJ/mol | ΔG_rxn^0 | -91.5 kJ/mol - -948.4 kJ/mol = 856.9 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: H_2O + N_2 ⟶ H_2O_2 + NH_2NH_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: 4 H_2O + N_2 ⟶ 2 H_2O_2 + NH_2NH_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 H_2O | 4 | -4 N_2 | 1 | -1 H_2O_2 | 2 | 2 NH_2NH_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) N_2 | 1 | -1 | ([N2])^(-1) H_2O_2 | 2 | 2 | ([H2O2])^2 NH_2NH_2 | 1 | 1 | [NH2NH2] 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 = ([H2O])^(-4) ([N2])^(-1) ([H2O2])^2 [NH2NH2] = (([H2O2])^2 [NH2NH2])/(([H2O])^4 [N2])

Construct the rate of reaction expression for: H_2O + N_2 ⟶ H_2O_2 + NH_2NH_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: 4 H_2O + N_2 ⟶ 2 H_2O_2 + NH_2NH_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 H_2O | 4 | -4 N_2 | 1 | -1 H_2O_2 | 2 | 2 NH_2NH_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 H_2O | 4 | -4 | -1/4 (Δ[H2O])/(Δt) N_2 | 1 | -1 | -(Δ[N2])/(Δt) H_2O_2 | 2 | 2 | 1/2 (Δ[H2O2])/(Δt) NH_2NH_2 | 1 | 1 | (Δ[NH2NH2])/(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 = -1/4 (Δ[H2O])/(Δt) = -(Δ[N2])/(Δt) = 1/2 (Δ[H2O2])/(Δt) = (Δ[NH2NH2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitrogen | hydrogen peroxide | diazane formula | H_2O | N_2 | H_2O_2 | NH_2NH_2 Hill formula | H_2O | N_2 | H_2O_2 | H_4N_2 name | water | nitrogen | hydrogen peroxide | diazane IUPAC name | water | molecular nitrogen | hydrogen peroxide | hydrazine

| water | nitrogen | hydrogen peroxide | diazane molar mass | 18.015 g/mol | 28.014 g/mol | 34.014 g/mol | 32.046 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) | liquid (at STP) melting point | 0 °C | -210 °C | -0.43 °C | 1 °C boiling point | 99.9839 °C | -195.79 °C | 150.2 °C | 113.5 °C density | 1 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | 1.44 g/cm^3 | 1.011 g/cm^3 solubility in water | | insoluble | miscible | miscible surface tension | 0.0728 N/m | 0.0066 N/m | 0.0804 N/m | 0.0667 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | 0.001249 Pa s (at 20 °C) | 8.76×10^-4 Pa s (at 25 °C) odor | odorless | odorless | |