AlCl3 = Cl2 + Al

AlCl_3 aluminum chloride ⟶ Cl_2 chlorine + Al aluminum

Balance the chemical equation algebraically: AlCl_3 ⟶ Cl_2 + Al Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AlCl_3 ⟶ c_2 Cl_2 + c_3 Al Set the number of atoms in the reactants equal to the number of atoms in the products for Al and Cl: Al: | c_1 = c_3 Cl: | 3 c_1 = 2 c_2 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 = 3/2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 AlCl_3 ⟶ 3 Cl_2 + 2 Al

⟶ +

aluminum chloride ⟶ chlorine + aluminum

| aluminum chloride | chlorine | aluminum molecular enthalpy | -704.2 kJ/mol | 0 kJ/mol | 0 kJ/mol total enthalpy | -1408 kJ/mol | 0 kJ/mol | 0 kJ/mol | H_initial = -1408 kJ/mol | H_final = 0 kJ/mol | ΔH_rxn^0 | 0 kJ/mol - -1408 kJ/mol = 1408 kJ/mol (endothermic) | |

| aluminum chloride | chlorine | aluminum molecular entropy | 111 J/(mol K) | 223 J/(mol K) | 28.3 J/(mol K) total entropy | 222 J/(mol K) | 669 J/(mol K) | 56.6 J/(mol K) | S_initial = 222 J/(mol K) | S_final = 725.6 J/(mol K) | ΔS_rxn^0 | 725.6 J/(mol K) - 222 J/(mol K) = 503.6 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: AlCl_3 ⟶ Cl_2 + 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: 2 AlCl_3 ⟶ 3 Cl_2 + 2 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 AlCl_3 | 2 | -2 Cl_2 | 3 | 3 Al | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AlCl_3 | 2 | -2 | ([AlCl3])^(-2) Cl_2 | 3 | 3 | ([Cl2])^3 Al | 2 | 2 | ([Al])^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 = ([AlCl3])^(-2) ([Cl2])^3 ([Al])^2 = (([Cl2])^3 ([Al])^2)/([AlCl3])^2

Construct the rate of reaction expression for: AlCl_3 ⟶ Cl_2 + 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: 2 AlCl_3 ⟶ 3 Cl_2 + 2 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 AlCl_3 | 2 | -2 Cl_2 | 3 | 3 Al | 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 AlCl_3 | 2 | -2 | -1/2 (Δ[AlCl3])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(Δt) Al | 2 | 2 | 1/2 (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 = -1/2 (Δ[AlCl3])/(Δt) = 1/3 (Δ[Cl2])/(Δt) = 1/2 (Δ[Al])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum chloride | chlorine | aluminum formula | AlCl_3 | Cl_2 | Al name | aluminum chloride | chlorine | aluminum IUPAC name | trichloroalumane | molecular chlorine | aluminum

| aluminum chloride | chlorine | aluminum molar mass | 133.3 g/mol | 70.9 g/mol | 26.9815385 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) melting point | 190 °C | -101 °C | 660.4 °C boiling point | | -34 °C | 2460 °C density | | 0.003214 g/cm^3 (at 0 °C) | 2.7 g/cm^3 solubility in water | | | insoluble surface tension | | | 0.817 N/m dynamic viscosity | | | 1.5×10^-4 Pa s (at 760 °C) odor | | | odorless