HCl + Ca(OH)2 + NaHCO3 = H2O + NaOH + NaCl + CaCO3

HCl hydrogen chloride + Ca(OH)_2 calcium hydroxide + NaHCO_3 sodium bicarbonate ⟶ H_2O water + NaOH sodium hydroxide + NaCl sodium chloride + CaCO_3 calcium carbonate

Balance the chemical equation algebraically: HCl + Ca(OH)_2 + NaHCO_3 ⟶ H_2O + NaOH + NaCl + CaCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Ca(OH)_2 + c_3 NaHCO_3 ⟶ c_4 H_2O + c_5 NaOH + c_6 NaCl + c_7 CaCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Ca, O, C and Na: Cl: | c_1 = c_6 H: | c_1 + 2 c_2 + c_3 = 2 c_4 + c_5 Ca: | c_2 = c_7 O: | 2 c_2 + 3 c_3 = c_4 + c_5 + 3 c_7 C: | c_3 = c_7 Na: | c_3 = c_5 + c_6 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_3 = c_2 c_4 = c_2 + 1 c_5 = c_2 - 1 c_6 = 1 c_7 = c_2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 2 and solve for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 3 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HCl + 2 Ca(OH)_2 + 2 NaHCO_3 ⟶ 3 H_2O + NaOH + NaCl + 2 CaCO_3

+ + ⟶ + + +

hydrogen chloride + calcium hydroxide + sodium bicarbonate ⟶ water + sodium hydroxide + sodium chloride + calcium carbonate

| hydrogen chloride | calcium hydroxide | sodium bicarbonate | water | sodium hydroxide | sodium chloride | calcium carbonate molecular enthalpy | -92.3 kJ/mol | -985.2 kJ/mol | -950.8 kJ/mol | -285.8 kJ/mol | -425.8 kJ/mol | -411.2 kJ/mol | -1208 kJ/mol total enthalpy | -92.3 kJ/mol | -1970 kJ/mol | -1902 kJ/mol | -857.5 kJ/mol | -425.8 kJ/mol | -411.2 kJ/mol | -2415 kJ/mol | H_initial = -3964 kJ/mol | | | H_final = -4110 kJ/mol | | | ΔH_rxn^0 | -4110 kJ/mol - -3964 kJ/mol = -145.4 kJ/mol (exothermic) | | | | | |

| hydrogen chloride | calcium hydroxide | sodium bicarbonate | water | sodium hydroxide | sodium chloride | calcium carbonate molecular free energy | -95.3 kJ/mol | -897.5 kJ/mol | -851 kJ/mol | -237.1 kJ/mol | -379.7 kJ/mol | -384.1 kJ/mol | -1129 kJ/mol total free energy | -95.3 kJ/mol | -1795 kJ/mol | -1702 kJ/mol | -711.3 kJ/mol | -379.7 kJ/mol | -384.1 kJ/mol | -2258 kJ/mol | G_initial = -3592 kJ/mol | | | G_final = -3733 kJ/mol | | | ΔG_rxn^0 | -3733 kJ/mol - -3592 kJ/mol = -141 kJ/mol (exergonic) | | | | | |

| hydrogen chloride | calcium hydroxide | sodium bicarbonate | water | sodium hydroxide | sodium chloride | calcium carbonate molecular entropy | 187 J/(mol K) | 83 J/(mol K) | 102 J/(mol K) | 69.91 J/(mol K) | 64 J/(mol K) | 72 J/(mol K) | 91.7 J/(mol K) total entropy | 187 J/(mol K) | 166 J/(mol K) | 204 J/(mol K) | 209.7 J/(mol K) | 64 J/(mol K) | 72 J/(mol K) | 183.4 J/(mol K) | S_initial = 557 J/(mol K) | | | S_final = 529.1 J/(mol K) | | | ΔS_rxn^0 | 529.1 J/(mol K) - 557 J/(mol K) = -27.87 J/(mol K) (exoentropic) | | | | | |

Construct the equilibrium constant, K, expression for: HCl + Ca(OH)_2 + NaHCO_3 ⟶ H_2O + NaOH + NaCl + CaCO_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: HCl + 2 Ca(OH)_2 + 2 NaHCO_3 ⟶ 3 H_2O + NaOH + NaCl + 2 CaCO_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 HCl | 1 | -1 Ca(OH)_2 | 2 | -2 NaHCO_3 | 2 | -2 H_2O | 3 | 3 NaOH | 1 | 1 NaCl | 1 | 1 CaCO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 1 | -1 | ([HCl])^(-1) Ca(OH)_2 | 2 | -2 | ([Ca(OH)2])^(-2) NaHCO_3 | 2 | -2 | ([NaHCO3])^(-2) H_2O | 3 | 3 | ([H2O])^3 NaOH | 1 | 1 | [NaOH] NaCl | 1 | 1 | [NaCl] CaCO_3 | 2 | 2 | ([CaCO3])^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 = ([HCl])^(-1) ([Ca(OH)2])^(-2) ([NaHCO3])^(-2) ([H2O])^3 [NaOH] [NaCl] ([CaCO3])^2 = (([H2O])^3 [NaOH] [NaCl] ([CaCO3])^2)/([HCl] ([Ca(OH)2])^2 ([NaHCO3])^2)

Construct the rate of reaction expression for: HCl + Ca(OH)_2 + NaHCO_3 ⟶ H_2O + NaOH + NaCl + CaCO_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: HCl + 2 Ca(OH)_2 + 2 NaHCO_3 ⟶ 3 H_2O + NaOH + NaCl + 2 CaCO_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 HCl | 1 | -1 Ca(OH)_2 | 2 | -2 NaHCO_3 | 2 | -2 H_2O | 3 | 3 NaOH | 1 | 1 NaCl | 1 | 1 CaCO_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 HCl | 1 | -1 | -(Δ[HCl])/(Δt) Ca(OH)_2 | 2 | -2 | -1/2 (Δ[Ca(OH)2])/(Δt) NaHCO_3 | 2 | -2 | -1/2 (Δ[NaHCO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NaOH | 1 | 1 | (Δ[NaOH])/(Δt) NaCl | 1 | 1 | (Δ[NaCl])/(Δt) CaCO_3 | 2 | 2 | 1/2 (Δ[CaCO3])/(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[HCl])/(Δt) = -1/2 (Δ[Ca(OH)2])/(Δt) = -1/2 (Δ[NaHCO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[NaOH])/(Δt) = (Δ[NaCl])/(Δt) = 1/2 (Δ[CaCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | calcium hydroxide | sodium bicarbonate | water | sodium hydroxide | sodium chloride | calcium carbonate formula | HCl | Ca(OH)_2 | NaHCO_3 | H_2O | NaOH | NaCl | CaCO_3 Hill formula | ClH | CaH_2O_2 | CHNaO_3 | H_2O | HNaO | ClNa | CCaO_3 name | hydrogen chloride | calcium hydroxide | sodium bicarbonate | water | sodium hydroxide | sodium chloride | calcium carbonate IUPAC name | hydrogen chloride | calcium dihydroxide | sodium hydrogen carbonate | water | sodium hydroxide | sodium chloride | calcium carbonate