HNO3 + (NH4)2CO3 = H2O + CO2 + NH4NO3

HNO_3 nitric acid + (NH_4)_2CO_3 ammonium carbonate ⟶ H_2O water + CO_2 carbon dioxide + NH_4NO_3 ammonium nitrate

Balance the chemical equation algebraically: HNO_3 + (NH_4)_2CO_3 ⟶ H_2O + CO_2 + NH_4NO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 (NH_4)_2CO_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 NH_4NO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and C: H: | c_1 + 8 c_2 = 2 c_3 + 4 c_5 N: | c_1 + 2 c_2 = 2 c_5 O: | 3 c_1 + 3 c_2 = c_3 + 2 c_4 + 3 c_5 C: | 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + (NH_4)_2CO_3 ⟶ H_2O + CO_2 + 2 NH_4NO_3

+ ⟶ + +

nitric acid + ammonium carbonate ⟶ water + carbon dioxide + ammonium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + (NH_4)_2CO_3 ⟶ H_2O + CO_2 + 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 HNO_3 + (NH_4)_2CO_3 ⟶ H_2O + CO_2 + 2 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 HNO_3 | 2 | -2 (NH_4)_2CO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 NH_4NO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) (NH_4)_2CO_3 | 1 | -1 | ([(NH4)2CO3])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] NH_4NO_3 | 2 | 2 | ([NH4NO3])^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 = ([HNO3])^(-2) ([(NH4)2CO3])^(-1) [H2O] [CO2] ([NH4NO3])^2 = ([H2O] [CO2] ([NH4NO3])^2)/(([HNO3])^2 [(NH4)2CO3])

Construct the rate of reaction expression for: HNO_3 + (NH_4)_2CO_3 ⟶ H_2O + CO_2 + 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 HNO_3 + (NH_4)_2CO_3 ⟶ H_2O + CO_2 + 2 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 HNO_3 | 2 | -2 (NH_4)_2CO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 NH_4NO_3 | 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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) (NH_4)_2CO_3 | 1 | -1 | -(Δ[(NH4)2CO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) NH_4NO_3 | 2 | 2 | 1/2 (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[HNO3])/(Δt) = -(Δ[(NH4)2CO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[NH4NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | ammonium carbonate | water | carbon dioxide | ammonium nitrate formula | HNO_3 | (NH_4)_2CO_3 | H_2O | CO_2 | NH_4NO_3 Hill formula | HNO_3 | CH_8N_2O_3 | H_2O | CO_2 | H_4N_2O_3 name | nitric acid | ammonium carbonate | water | carbon dioxide | ammonium nitrate