H2O + CO2 + NH3 = (NH4)2CO3

H_2O water + CO_2 carbon dioxide + NH_3 ammonia ⟶ (NH_4)_2CO_3 ammonium carbonate

Balance the chemical equation algebraically: H_2O + CO_2 + NH_3 ⟶ (NH_4)_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CO_2 + c_3 NH_3 ⟶ c_4 (NH_4)_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C and N: H: | 2 c_1 + 3 c_3 = 8 c_4 O: | c_1 + 2 c_2 = 3 c_4 C: | c_2 = c_4 N: | c_3 = 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 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + CO_2 + 2 NH_3 ⟶ (NH_4)_2CO_3

+ + ⟶

water + carbon dioxide + ammonia ⟶ ammonium carbonate

Construct the equilibrium constant, K, expression for: H_2O + CO_2 + NH_3 ⟶ (NH_4)_2CO_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: H_2O + CO_2 + 2 NH_3 ⟶ (NH_4)_2CO_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 | 1 | -1 CO_2 | 1 | -1 NH_3 | 2 | -2 (NH_4)_2CO_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 | 1 | -1 | ([H2O])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) NH_3 | 2 | -2 | ([NH3])^(-2) (NH_4)_2CO_3 | 1 | 1 | [(NH4)2CO3] 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])^(-1) ([CO2])^(-1) ([NH3])^(-2) [(NH4)2CO3] = ([(NH4)2CO3])/([H2O] [CO2] ([NH3])^2)

Construct the rate of reaction expression for: H_2O + CO_2 + NH_3 ⟶ (NH_4)_2CO_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: H_2O + CO_2 + 2 NH_3 ⟶ (NH_4)_2CO_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 | 1 | -1 CO_2 | 1 | -1 NH_3 | 2 | -2 (NH_4)_2CO_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 | 1 | -1 | -(Δ[H2O])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) (NH_4)_2CO_3 | 1 | 1 | (Δ[(NH4)2CO3])/(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[H2O])/(Δt) = -(Δ[CO2])/(Δt) = -1/2 (Δ[NH3])/(Δt) = (Δ[(NH4)2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | carbon dioxide | ammonia | ammonium carbonate formula | H_2O | CO_2 | NH_3 | (NH_4)_2CO_3 Hill formula | H_2O | CO_2 | H_3N | CH_8N_2O_3 name | water | carbon dioxide | ammonia | ammonium carbonate