NaHCO3 + Ba(OH)2 = H2O + NaOH + BaCO3

NaHCO_3 sodium bicarbonate + Ba(OH)_2 barium hydroxide ⟶ H_2O water + NaOH sodium hydroxide + BaCO_3 barium carbonate

Balance the chemical equation algebraically: NaHCO_3 + Ba(OH)_2 ⟶ H_2O + NaOH + BaCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaHCO_3 + c_2 Ba(OH)_2 ⟶ c_3 H_2O + c_4 NaOH + c_5 BaCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, Na, O and Ba: C: | c_1 = c_5 H: | c_1 + 2 c_2 = 2 c_3 + c_4 Na: | c_1 = c_4 O: | 3 c_1 + 2 c_2 = c_3 + c_4 + 3 c_5 Ba: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NaHCO_3 + Ba(OH)_2 ⟶ H_2O + NaOH + BaCO_3

+ ⟶ + +

sodium bicarbonate + barium hydroxide ⟶ water + sodium hydroxide + barium carbonate

| sodium bicarbonate | barium hydroxide | water | sodium hydroxide | barium carbonate molecular enthalpy | -950.8 kJ/mol | -944.7 kJ/mol | -285.8 kJ/mol | -425.8 kJ/mol | -1213 kJ/mol total enthalpy | -950.8 kJ/mol | -944.7 kJ/mol | -285.8 kJ/mol | -425.8 kJ/mol | -1213 kJ/mol | H_initial = -1896 kJ/mol | | H_final = -1925 kJ/mol | | ΔH_rxn^0 | -1925 kJ/mol - -1896 kJ/mol = -29.13 kJ/mol (exothermic) | | | |

Construct the equilibrium constant, K, expression for: NaHCO_3 + Ba(OH)_2 ⟶ H_2O + NaOH + BaCO_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: NaHCO_3 + Ba(OH)_2 ⟶ H_2O + NaOH + BaCO_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 NaHCO_3 | 1 | -1 Ba(OH)_2 | 1 | -1 H_2O | 1 | 1 NaOH | 1 | 1 BaCO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaHCO_3 | 1 | -1 | ([NaHCO3])^(-1) Ba(OH)_2 | 1 | -1 | ([Ba(OH)2])^(-1) H_2O | 1 | 1 | [H2O] NaOH | 1 | 1 | [NaOH] BaCO_3 | 1 | 1 | [BaCO3] 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 = ([NaHCO3])^(-1) ([Ba(OH)2])^(-1) [H2O] [NaOH] [BaCO3] = ([H2O] [NaOH] [BaCO3])/([NaHCO3] [Ba(OH)2])

Construct the rate of reaction expression for: NaHCO_3 + Ba(OH)_2 ⟶ H_2O + NaOH + BaCO_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: NaHCO_3 + Ba(OH)_2 ⟶ H_2O + NaOH + BaCO_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 NaHCO_3 | 1 | -1 Ba(OH)_2 | 1 | -1 H_2O | 1 | 1 NaOH | 1 | 1 BaCO_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 NaHCO_3 | 1 | -1 | -(Δ[NaHCO3])/(Δt) Ba(OH)_2 | 1 | -1 | -(Δ[Ba(OH)2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NaOH | 1 | 1 | (Δ[NaOH])/(Δt) BaCO_3 | 1 | 1 | (Δ[BaCO3])/(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[NaHCO3])/(Δt) = -(Δ[Ba(OH)2])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NaOH])/(Δt) = (Δ[BaCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium bicarbonate | barium hydroxide | water | sodium hydroxide | barium carbonate formula | NaHCO_3 | Ba(OH)_2 | H_2O | NaOH | BaCO_3 Hill formula | CHNaO_3 | BaH_2O_2 | H_2O | HNaO | CBaO_3 name | sodium bicarbonate | barium hydroxide | water | sodium hydroxide | barium carbonate IUPAC name | sodium hydrogen carbonate | barium(+2) cation dihydroxide | water | sodium hydroxide | barium(+2) cation carbonate

| sodium bicarbonate | barium hydroxide | water | sodium hydroxide | barium carbonate molar mass | 84.006 g/mol | 171.34 g/mol | 18.015 g/mol | 39.997 g/mol | 197.33 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 270 °C | 300 °C | 0 °C | 323 °C | 1350 °C boiling point | | | 99.9839 °C | 1390 °C | density | 2.16 g/cm^3 | 2.2 g/cm^3 | 1 g/cm^3 | 2.13 g/cm^3 | 3.89 g/cm^3 solubility in water | soluble | | | soluble | insoluble surface tension | | | 0.0728 N/m | 0.07435 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 0.004 Pa s (at 350 °C) | odor | odorless | | odorless | | odorless