Cl2 + Al = AlCl3

Cl_2 (chlorine) + Al (aluminum) ⟶ AlCl_3 (aluminum chloride)

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

+ ⟶

chlorine + aluminum ⟶ aluminum chloride

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

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

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

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

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

| chlorine | aluminum | aluminum chloride molar mass | 70.9 g/mol | 26.9815385 g/mol | 133.3 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) melting point | -101 °C | 660.4 °C | 190 °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 |