H2 + Al2O3 = H2O + Al

H_2 (hydrogen) + Al_2O_3 (aluminum oxide) ⟶ H_2O (water) + Al (aluminum)

Balance the chemical equation algebraically: H_2 + Al_2O_3 ⟶ H_2O + Al Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 Al_2O_3 ⟶ c_3 H_2O + c_4 Al Set the number of atoms in the reactants equal to the number of atoms in the products for H, Al and O: H: | 2 c_1 = 2 c_3 Al: | 2 c_2 = c_4 O: | 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2 + Al_2O_3 ⟶ 3 H_2O + 2 Al

+ ⟶ +

hydrogen + aluminum oxide ⟶ water + aluminum

| hydrogen | aluminum oxide | water | aluminum molecular enthalpy | 0 kJ/mol | -1676 kJ/mol | -285.8 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -1676 kJ/mol | -857.5 kJ/mol | 0 kJ/mol | H_initial = -1676 kJ/mol | | H_final = -857.5 kJ/mol | ΔH_rxn^0 | -857.5 kJ/mol - -1676 kJ/mol = 818.5 kJ/mol (endothermic) | | |

| hydrogen | aluminum oxide | water | aluminum molecular entropy | 115 J/(mol K) | 51 J/(mol K) | 69.91 J/(mol K) | 28.3 J/(mol K) total entropy | 345 J/(mol K) | 51 J/(mol K) | 209.7 J/(mol K) | 56.6 J/(mol K) | S_initial = 396 J/(mol K) | | S_final = 266.3 J/(mol K) | ΔS_rxn^0 | 266.3 J/(mol K) - 396 J/(mol K) = -129.7 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2 + Al_2O_3 ⟶ H_2O + 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 H_2 + Al_2O_3 ⟶ 3 H_2O + 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 H_2 | 3 | -3 Al_2O_3 | 1 | -1 H_2O | 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 H_2 | 3 | -3 | ([H2])^(-3) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) H_2O | 3 | 3 | ([H2O])^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 = ([H2])^(-3) ([Al2O3])^(-1) ([H2O])^3 ([Al])^2 = (([H2O])^3 ([Al])^2)/(([H2])^3 [Al2O3])

Construct the rate of reaction expression for: H_2 + Al_2O_3 ⟶ H_2O + 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 H_2 + Al_2O_3 ⟶ 3 H_2O + 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 H_2 | 3 | -3 Al_2O_3 | 1 | -1 H_2O | 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 H_2 | 3 | -3 | -1/3 (Δ[H2])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(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 = -1/3 (Δ[H2])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[Al])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | aluminum oxide | water | aluminum formula | H_2 | Al_2O_3 | H_2O | Al name | hydrogen | aluminum oxide | water | aluminum IUPAC name | molecular hydrogen | dialuminum;oxygen(2-) | water | aluminum

| hydrogen | aluminum oxide | water | aluminum molar mass | 2.016 g/mol | 101.96 g/mol | 18.015 g/mol | 26.9815385 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -259.2 °C | 2040 °C | 0 °C | 660.4 °C boiling point | -252.8 °C | | 99.9839 °C | 2460 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | | 1 g/cm^3 | 2.7 g/cm^3 solubility in water | | | | insoluble surface tension | | | 0.0728 N/m | 0.817 N/m dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.5×10^-4 Pa s (at 760 °C) odor | odorless | odorless | odorless | odorless