Cl2 + NaOH = H2O + NaCl + NaClO4

Cl_2 chlorine + NaOH sodium hydroxide ⟶ H_2O water + NaCl sodium chloride + NaClO_4 sodium perchlorate

Balance the chemical equation algebraically: Cl_2 + NaOH ⟶ H_2O + NaCl + NaClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 NaOH ⟶ c_3 H_2O + c_4 NaCl + c_5 NaClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Na and O: Cl: | 2 c_1 = c_4 + c_5 H: | c_2 = 2 c_3 Na: | c_2 = c_4 + c_5 O: | c_2 = c_3 + 4 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 8 c_3 = 4 c_4 = 7 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Cl_2 + 8 NaOH ⟶ 4 H_2O + 7 NaCl + NaClO_4

+ ⟶ + +

chlorine + sodium hydroxide ⟶ water + sodium chloride + sodium perchlorate

| chlorine | sodium hydroxide | water | sodium chloride | sodium perchlorate molecular enthalpy | 0 kJ/mol | -425.8 kJ/mol | -285.8 kJ/mol | -411.2 kJ/mol | -383.3 kJ/mol total enthalpy | 0 kJ/mol | -3406 kJ/mol | -1143 kJ/mol | -2878 kJ/mol | -383.3 kJ/mol | H_initial = -3406 kJ/mol | | H_final = -4405 kJ/mol | | ΔH_rxn^0 | -4405 kJ/mol - -3406 kJ/mol = -998.6 kJ/mol (exothermic) | | | |

| chlorine | sodium hydroxide | water | sodium chloride | sodium perchlorate molecular free energy | 0 kJ/mol | -379.7 kJ/mol | -237.1 kJ/mol | -384.1 kJ/mol | -254.9 kJ/mol total free energy | 0 kJ/mol | -3038 kJ/mol | -948.4 kJ/mol | -2689 kJ/mol | -254.9 kJ/mol | G_initial = -3038 kJ/mol | | G_final = -3892 kJ/mol | | ΔG_rxn^0 | -3892 kJ/mol - -3038 kJ/mol = -854.4 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: Cl_2 + NaOH ⟶ H_2O + NaCl + NaClO_4 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: 4 Cl_2 + 8 NaOH ⟶ 4 H_2O + 7 NaCl + NaClO_4 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 Cl_2 | 4 | -4 NaOH | 8 | -8 H_2O | 4 | 4 NaCl | 7 | 7 NaClO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 4 | -4 | ([Cl2])^(-4) NaOH | 8 | -8 | ([NaOH])^(-8) H_2O | 4 | 4 | ([H2O])^4 NaCl | 7 | 7 | ([NaCl])^7 NaClO_4 | 1 | 1 | [NaClO4] 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 = ([Cl2])^(-4) ([NaOH])^(-8) ([H2O])^4 ([NaCl])^7 [NaClO4] = (([H2O])^4 ([NaCl])^7 [NaClO4])/(([Cl2])^4 ([NaOH])^8)

Construct the rate of reaction expression for: Cl_2 + NaOH ⟶ H_2O + NaCl + NaClO_4 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: 4 Cl_2 + 8 NaOH ⟶ 4 H_2O + 7 NaCl + NaClO_4 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 Cl_2 | 4 | -4 NaOH | 8 | -8 H_2O | 4 | 4 NaCl | 7 | 7 NaClO_4 | 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 Cl_2 | 4 | -4 | -1/4 (Δ[Cl2])/(Δt) NaOH | 8 | -8 | -1/8 (Δ[NaOH])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NaCl | 7 | 7 | 1/7 (Δ[NaCl])/(Δt) NaClO_4 | 1 | 1 | (Δ[NaClO4])/(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 = -1/4 (Δ[Cl2])/(Δt) = -1/8 (Δ[NaOH])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/7 (Δ[NaCl])/(Δt) = (Δ[NaClO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | sodium hydroxide | water | sodium chloride | sodium perchlorate formula | Cl_2 | NaOH | H_2O | NaCl | NaClO_4 Hill formula | Cl_2 | HNaO | H_2O | ClNa | ClNaO_4 name | chlorine | sodium hydroxide | water | sodium chloride | sodium perchlorate IUPAC name | molecular chlorine | sodium hydroxide | water | sodium chloride | sodium perchlorate