NH4OH + H2CO3 = H2O + (NH4)2CO3

NH_4OH (ammonium hydroxide) + H_2CO_3 (carbonic acid) ⟶ H_2O (water) + (NH_4)_2CO_3 (ammonium carbonate)

Balance the chemical equation algebraically: NH_4OH + H_2CO_3 ⟶ H_2O + (NH_4)_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4OH + c_2 H_2CO_3 ⟶ c_3 H_2O + 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, N, O and C: H: | 5 c_1 + 2 c_2 = 2 c_3 + 8 c_4 N: | c_1 = 2 c_4 O: | c_1 + 3 c_2 = c_3 + 3 c_4 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 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_4OH + H_2CO_3 ⟶ 2 H_2O + (NH_4)_2CO_3

+ ⟶ +

ammonium hydroxide + carbonic acid ⟶ water + ammonium carbonate

Construct the equilibrium constant, K, expression for: NH_4OH + H_2CO_3 ⟶ H_2O + (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: 2 NH_4OH + H_2CO_3 ⟶ 2 H_2O + (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 NH_4OH | 2 | -2 H_2CO_3 | 1 | -1 H_2O | 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 NH_4OH | 2 | -2 | ([NH4OH])^(-2) H_2CO_3 | 1 | -1 | ([H2CO3])^(-1) H_2O | 2 | 2 | ([H2O])^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 = ([NH4OH])^(-2) ([H2CO3])^(-1) ([H2O])^2 [(NH4)2CO3] = (([H2O])^2 [(NH4)2CO3])/(([NH4OH])^2 [H2CO3])

Construct the rate of reaction expression for: NH_4OH + H_2CO_3 ⟶ H_2O + (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: 2 NH_4OH + H_2CO_3 ⟶ 2 H_2O + (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 NH_4OH | 2 | -2 H_2CO_3 | 1 | -1 H_2O | 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 NH_4OH | 2 | -2 | -1/2 (Δ[NH4OH])/(Δt) H_2CO_3 | 1 | -1 | -(Δ[H2CO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(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 = -1/2 (Δ[NH4OH])/(Δt) = -(Δ[H2CO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[(NH4)2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium hydroxide | carbonic acid | water | ammonium carbonate formula | NH_4OH | H_2CO_3 | H_2O | (NH_4)_2CO_3 Hill formula | H_5NO | CH_2O_3 | H_2O | CH_8N_2O_3 name | ammonium hydroxide | carbonic acid | water | ammonium carbonate

| ammonium hydroxide | carbonic acid | water | ammonium carbonate molar mass | 35.046 g/mol | 62.024 g/mol | 18.015 g/mol | 96.09 g/mol phase | aqueous (at STP) | | liquid (at STP) | solid (at STP) melting point | -57.5 °C | | 0 °C | 58 °C boiling point | 36 °C | | 99.9839 °C | density | 0.9 g/cm^3 | | 1 g/cm^3 | 1.5 g/cm^3 solubility in water | very soluble | | | soluble surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |