Na + AlCl3 = NaCl + Al

Na sodium + AlCl_3 aluminum chloride ⟶ NaCl sodium chloride + Al aluminum

Balance the chemical equation algebraically: Na + AlCl_3 ⟶ NaCl + Al Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 AlCl_3 ⟶ c_3 NaCl + c_4 Al Set the number of atoms in the reactants equal to the number of atoms in the products for Na, Al and Cl: Na: | c_1 = c_3 Al: | c_2 = c_4 Cl: | 3 c_2 = c_3 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Na + AlCl_3 ⟶ 3 NaCl + Al

+ ⟶ +

sodium + aluminum chloride ⟶ sodium chloride + aluminum

| sodium | aluminum chloride | sodium chloride | aluminum molecular enthalpy | 0 kJ/mol | -704.2 kJ/mol | -411.2 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -704.2 kJ/mol | -1234 kJ/mol | 0 kJ/mol | H_initial = -704.2 kJ/mol | | H_final = -1234 kJ/mol | ΔH_rxn^0 | -1234 kJ/mol - -704.2 kJ/mol = -529.4 kJ/mol (exothermic) | | |

| sodium | aluminum chloride | sodium chloride | aluminum molecular entropy | 51 J/(mol K) | 111 J/(mol K) | 72 J/(mol K) | 28.3 J/(mol K) total entropy | 153 J/(mol K) | 111 J/(mol K) | 216 J/(mol K) | 28.3 J/(mol K) | S_initial = 264 J/(mol K) | | S_final = 244.3 J/(mol K) | ΔS_rxn^0 | 244.3 J/(mol K) - 264 J/(mol K) = -19.7 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: Na + AlCl_3 ⟶ NaCl + Al 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: 3 Na + AlCl_3 ⟶ 3 NaCl + Al 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 Na | 3 | -3 AlCl_3 | 1 | -1 NaCl | 3 | 3 Al | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 3 | -3 | ([Na])^(-3) AlCl_3 | 1 | -1 | ([AlCl3])^(-1) NaCl | 3 | 3 | ([NaCl])^3 Al | 1 | 1 | [Al] 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 = ([Na])^(-3) ([AlCl3])^(-1) ([NaCl])^3 [Al] = (([NaCl])^3 [Al])/(([Na])^3 [AlCl3])

Construct the rate of reaction expression for: Na + AlCl_3 ⟶ NaCl + Al 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: 3 Na + AlCl_3 ⟶ 3 NaCl + Al 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 Na | 3 | -3 AlCl_3 | 1 | -1 NaCl | 3 | 3 Al | 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 Na | 3 | -3 | -1/3 (Δ[Na])/(Δt) AlCl_3 | 1 | -1 | -(Δ[AlCl3])/(Δt) NaCl | 3 | 3 | 1/3 (Δ[NaCl])/(Δt) Al | 1 | 1 | (Δ[Al])/(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 = -1/3 (Δ[Na])/(Δt) = -(Δ[AlCl3])/(Δt) = 1/3 (Δ[NaCl])/(Δt) = (Δ[Al])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | aluminum chloride | sodium chloride | aluminum formula | Na | AlCl_3 | NaCl | Al Hill formula | Na | AlCl_3 | ClNa | Al name | sodium | aluminum chloride | sodium chloride | aluminum IUPAC name | sodium | trichloroalumane | sodium chloride | aluminum