NaOH + (NH4)2CO3 = H2O + NH3 + Na2CO3

NaOH sodium hydroxide + (NH_4)_2CO_3 ammonium carbonate ⟶ H_2O water + NH_3 ammonia + Na_2CO_3 soda ash

Balance the chemical equation algebraically: NaOH + (NH_4)_2CO_3 ⟶ H_2O + NH_3 + Na_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 (NH_4)_2CO_3 ⟶ c_3 H_2O + c_4 NH_3 + c_5 Na_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, C and N: H: | c_1 + 8 c_2 = 2 c_3 + 3 c_4 Na: | c_1 = 2 c_5 O: | c_1 + 3 c_2 = c_3 + 3 c_5 C: | c_2 = c_5 N: | 2 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 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + (NH_4)_2CO_3 ⟶ 2 H_2O + 2 NH_3 + Na_2CO_3

+ ⟶ + +

sodium hydroxide + ammonium carbonate ⟶ water + ammonia + soda ash

Construct the equilibrium constant, K, expression for: NaOH + (NH_4)_2CO_3 ⟶ H_2O + NH_3 + Na_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 NaOH + (NH_4)_2CO_3 ⟶ 2 H_2O + 2 NH_3 + Na_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 NaOH | 2 | -2 (NH_4)_2CO_3 | 1 | -1 H_2O | 2 | 2 NH_3 | 2 | 2 Na_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 NaOH | 2 | -2 | ([NaOH])^(-2) (NH_4)_2CO_3 | 1 | -1 | ([(NH4)2CO3])^(-1) H_2O | 2 | 2 | ([H2O])^2 NH_3 | 2 | 2 | ([NH3])^2 Na_2CO_3 | 1 | 1 | [Na2CO3] 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 = ([NaOH])^(-2) ([(NH4)2CO3])^(-1) ([H2O])^2 ([NH3])^2 [Na2CO3] = (([H2O])^2 ([NH3])^2 [Na2CO3])/(([NaOH])^2 [(NH4)2CO3])

Construct the rate of reaction expression for: NaOH + (NH_4)_2CO_3 ⟶ H_2O + NH_3 + Na_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 NaOH + (NH_4)_2CO_3 ⟶ 2 H_2O + 2 NH_3 + Na_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 NaOH | 2 | -2 (NH_4)_2CO_3 | 1 | -1 H_2O | 2 | 2 NH_3 | 2 | 2 Na_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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) (NH_4)_2CO_3 | 1 | -1 | -(Δ[(NH4)2CO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NH_3 | 2 | 2 | 1/2 (Δ[NH3])/(Δt) Na_2CO_3 | 1 | 1 | (Δ[Na2CO3])/(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[NaOH])/(Δt) = -(Δ[(NH4)2CO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[NH3])/(Δt) = (Δ[Na2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | ammonium carbonate | water | ammonia | soda ash formula | NaOH | (NH_4)_2CO_3 | H_2O | NH_3 | Na_2CO_3 Hill formula | HNaO | CH_8N_2O_3 | H_2O | H_3N | CNa_2O_3 name | sodium hydroxide | ammonium carbonate | water | ammonia | soda ash IUPAC name | sodium hydroxide | | water | ammonia | disodium carbonate

| sodium hydroxide | ammonium carbonate | water | ammonia | soda ash molar mass | 39.997 g/mol | 96.09 g/mol | 18.015 g/mol | 17.031 g/mol | 105.99 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 323 °C | 58 °C | 0 °C | -77.73 °C | 851 °C boiling point | 1390 °C | | 99.9839 °C | -33.33 °C | 1600 °C density | 2.13 g/cm^3 | 1.5 g/cm^3 | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | solubility in water | soluble | soluble | | | soluble surface tension | 0.07435 N/m | | 0.0728 N/m | 0.0234 N/m | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | 0.00355 Pa s (at 900 °C) odor | | | odorless | |