Al + O2 -> Al2O3

Al aluminum + O_2 oxygen ⟶ Al_2O_3 aluminum oxide

Balance the chemical equation algebraically: Al + O_2 ⟶ Al_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 O_2 ⟶ c_3 Al_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al and O: Al: | c_1 = 2 c_3 O: | 2 c_2 = 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3/2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 3 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Al + 3 O_2 ⟶ 2 Al_2O_3

+ ⟶

aluminum + oxygen ⟶ aluminum oxide

| aluminum | oxygen | aluminum oxide molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -1676 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -3352 kJ/mol | H_initial = 0 kJ/mol | | H_final = -3352 kJ/mol ΔH_rxn^0 | -3352 kJ/mol - 0 kJ/mol = -3352 kJ/mol (exothermic) | |

| aluminum | oxygen | aluminum oxide molecular entropy | 28.3 J/(mol K) | 205 J/(mol K) | 51 J/(mol K) total entropy | 113.2 J/(mol K) | 615 J/(mol K) | 102 J/(mol K) | S_initial = 728.2 J/(mol K) | | S_final = 102 J/(mol K) ΔS_rxn^0 | 102 J/(mol K) - 728.2 J/(mol K) = -626.2 J/(mol K) (exoentropic) | |

Construct the equilibrium constant, K, expression for: Al + O_2 ⟶ Al_2O_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: 4 Al + 3 O_2 ⟶ 2 Al_2O_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 Al | 4 | -4 O_2 | 3 | -3 Al_2O_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 4 | -4 | ([Al])^(-4) O_2 | 3 | -3 | ([O2])^(-3) Al_2O_3 | 2 | 2 | ([Al2O3])^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 = ([Al])^(-4) ([O2])^(-3) ([Al2O3])^2 = ([Al2O3])^2/(([Al])^4 ([O2])^3)

Construct the rate of reaction expression for: Al + O_2 ⟶ Al_2O_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: 4 Al + 3 O_2 ⟶ 2 Al_2O_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 Al | 4 | -4 O_2 | 3 | -3 Al_2O_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 Al | 4 | -4 | -1/4 (Δ[Al])/(Δt) O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) Al_2O_3 | 2 | 2 | 1/2 (Δ[Al2O3])/(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[Al])/(Δt) = -1/3 (Δ[O2])/(Δt) = 1/2 (Δ[Al2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | oxygen | aluminum oxide formula | Al | O_2 | Al_2O_3 name | aluminum | oxygen | aluminum oxide IUPAC name | aluminum | molecular oxygen | dialuminum;oxygen(2-)

| aluminum | oxygen | aluminum oxide molar mass | 26.9815385 g/mol | 31.998 g/mol | 101.96 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) melting point | 660.4 °C | -218 °C | 2040 °C boiling point | 2460 °C | -183 °C | density | 2.7 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | solubility in water | insoluble | | surface tension | 0.817 N/m | 0.01347 N/m | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | odorless | odorless