H2O + N2O = NH4NO3

H_2O water + N_2O nitrous oxide ⟶ NH_4NO_3 ammonium nitrate

Balance the chemical equation algebraically: H_2O + N_2O ⟶ NH_4NO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 N_2O ⟶ c_3 NH_4NO_3 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 = 4 c_3 O: | c_1 + c_2 = 3 c_3 N: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + N_2O ⟶ NH_4NO_3

+ ⟶

water + nitrous oxide ⟶ ammonium nitrate

| water | nitrous oxide | ammonium nitrate molecular free energy | -237.1 kJ/mol | 104 kJ/mol | -183.9 kJ/mol total free energy | -474.2 kJ/mol | 104 kJ/mol | -183.9 kJ/mol | G_initial = -370.2 kJ/mol | | G_final = -183.9 kJ/mol ΔG_rxn^0 | -183.9 kJ/mol - -370.2 kJ/mol = 186.3 kJ/mol (endergonic) | |

Construct the equilibrium constant, K, expression for: H_2O + N_2O ⟶ NH_4NO_3 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 H_2O + N_2O ⟶ NH_4NO_3 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 | 2 | -2 N_2O | 1 | -1 NH_4NO_3 | 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 | 2 | -2 | ([H2O])^(-2) N_2O | 1 | -1 | ([N2O])^(-1) NH_4NO_3 | 1 | 1 | [NH4NO3] 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])^(-2) ([N2O])^(-1) [NH4NO3] = ([NH4NO3])/(([H2O])^2 [N2O])

Construct the rate of reaction expression for: H_2O + N_2O ⟶ NH_4NO_3 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 H_2O + N_2O ⟶ NH_4NO_3 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 | 2 | -2 N_2O | 1 | -1 NH_4NO_3 | 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) N_2O | 1 | -1 | -(Δ[N2O])/(Δt) NH_4NO_3 | 1 | 1 | (Δ[NH4NO3])/(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[H2O])/(Δt) = -(Δ[N2O])/(Δt) = (Δ[NH4NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitrous oxide | ammonium nitrate formula | H_2O | N_2O | NH_4NO_3 Hill formula | H_2O | N_2O | H_4N_2O_3 name | water | nitrous oxide | ammonium nitrate