H2 + Al = AlH3

H_2 hydrogen + Al aluminum ⟶ AlH3

Balance the chemical equation algebraically: H_2 + Al ⟶ AlH3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 Al ⟶ c_3 AlH3 Set the number of atoms in the reactants equal to the number of atoms in the products for H and Al: H: | 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 H_2 + 2 Al ⟶ 2 AlH3

+ ⟶ AlH3

hydrogen + aluminum ⟶ AlH3

Construct the equilibrium constant, K, expression for: H_2 + Al ⟶ AlH3 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 + 2 Al ⟶ 2 AlH3 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 | 2 | -2 AlH3 | 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 | 2 | -2 | ([Al])^(-2) AlH3 | 2 | 2 | ([AlH3])^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) ([Al])^(-2) ([AlH3])^2 = ([AlH3])^2/(([H2])^3 ([Al])^2)

Construct the rate of reaction expression for: H_2 + Al ⟶ AlH3 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 + 2 Al ⟶ 2 AlH3 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 | 2 | -2 AlH3 | 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 | 2 | -2 | -1/2 (Δ[Al])/(Δt) AlH3 | 2 | 2 | 1/2 (Δ[AlH3])/(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) = -1/2 (Δ[Al])/(Δt) = 1/2 (Δ[AlH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | aluminum | AlH3 formula | H_2 | Al | AlH3 Hill formula | H_2 | Al | H3Al name | hydrogen | aluminum | IUPAC name | molecular hydrogen | aluminum |

| hydrogen | aluminum | AlH3 molar mass | 2.016 g/mol | 26.9815385 g/mol | 30.006 g/mol phase | gas (at STP) | solid (at STP) | melting point | -259.2 °C | 660.4 °C | boiling point | -252.8 °C | 2460 °C | density | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.7 g/cm^3 | solubility in water | | insoluble | surface tension | | 0.817 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | 1.5×10^-4 Pa s (at 760 °C) | odor | odorless | odorless |