NH4NO3 + C12H14O4(NO3)6 = H2O + O2 + CO2 + N2

NH_4NO_3 ammonium nitrate + C12H14O4(NO3)6 ⟶ H_2O water + O_2 oxygen + CO_2 carbon dioxide + N_2 nitrogen

Balance the chemical equation algebraically: NH_4NO_3 + C12H14O4(NO3)6 ⟶ H_2O + O_2 + CO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4NO_3 + c_2 C12H14O4(NO3)6 ⟶ c_3 H_2O + c_4 O_2 + c_5 CO_2 + c_6 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and C: H: | 4 c_1 + 14 c_2 = 2 c_3 N: | 2 c_1 + 6 c_2 = 2 c_6 O: | 3 c_1 + 22 c_2 = c_3 + 2 c_4 + 2 c_5 C: | 12 c_2 = c_5 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_2 = 1 c_3 = 2 c_1 + 7 c_4 = c_1/2 - 9/2 c_5 = 12 c_6 = c_1 + 3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 11 and solve for the remaining coefficients: c_1 = 11 c_2 = 1 c_3 = 29 c_4 = 1 c_5 = 12 c_6 = 14 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 11 NH_4NO_3 + C12H14O4(NO3)6 ⟶ 29 H_2O + O_2 + 12 CO_2 + 14 N_2

+ C12H14O4(NO3)6 ⟶ + + +

ammonium nitrate + C12H14O4(NO3)6 ⟶ water + oxygen + carbon dioxide + nitrogen

Construct the equilibrium constant, K, expression for: NH_4NO_3 + C12H14O4(NO3)6 ⟶ H_2O + O_2 + CO_2 + N_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: 11 NH_4NO_3 + C12H14O4(NO3)6 ⟶ 29 H_2O + O_2 + 12 CO_2 + 14 N_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 NH_4NO_3 | 11 | -11 C12H14O4(NO3)6 | 1 | -1 H_2O | 29 | 29 O_2 | 1 | 1 CO_2 | 12 | 12 N_2 | 14 | 14 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4NO_3 | 11 | -11 | ([NH4NO3])^(-11) C12H14O4(NO3)6 | 1 | -1 | ([C12H14O4(NO3)6])^(-1) H_2O | 29 | 29 | ([H2O])^29 O_2 | 1 | 1 | [O2] CO_2 | 12 | 12 | ([CO2])^12 N_2 | 14 | 14 | ([N2])^14 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 = ([NH4NO3])^(-11) ([C12H14O4(NO3)6])^(-1) ([H2O])^29 [O2] ([CO2])^12 ([N2])^14 = (([H2O])^29 [O2] ([CO2])^12 ([N2])^14)/(([NH4NO3])^11 [C12H14O4(NO3)6])

Construct the rate of reaction expression for: NH_4NO_3 + C12H14O4(NO3)6 ⟶ H_2O + O_2 + CO_2 + N_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: 11 NH_4NO_3 + C12H14O4(NO3)6 ⟶ 29 H_2O + O_2 + 12 CO_2 + 14 N_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 NH_4NO_3 | 11 | -11 C12H14O4(NO3)6 | 1 | -1 H_2O | 29 | 29 O_2 | 1 | 1 CO_2 | 12 | 12 N_2 | 14 | 14 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 NH_4NO_3 | 11 | -11 | -1/11 (Δ[NH4NO3])/(Δt) C12H14O4(NO3)6 | 1 | -1 | -(Δ[C12H14O4(NO3)6])/(Δt) H_2O | 29 | 29 | 1/29 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) CO_2 | 12 | 12 | 1/12 (Δ[CO2])/(Δt) N_2 | 14 | 14 | 1/14 (Δ[N2])/(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 = -1/11 (Δ[NH4NO3])/(Δt) = -(Δ[C12H14O4(NO3)6])/(Δt) = 1/29 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/12 (Δ[CO2])/(Δt) = 1/14 (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium nitrate | C12H14O4(NO3)6 | water | oxygen | carbon dioxide | nitrogen formula | NH_4NO_3 | C12H14O4(NO3)6 | H_2O | O_2 | CO_2 | N_2 Hill formula | H_4N_2O_3 | C12H14N6O22 | H_2O | O_2 | CO_2 | N_2 name | ammonium nitrate | | water | oxygen | carbon dioxide | nitrogen IUPAC name | | | water | molecular oxygen | carbon dioxide | molecular nitrogen