H2 + Al + SiO2 = Al2O3 + SiH4

H_2 hydrogen + Al aluminum + SiO_2 silicon dioxide ⟶ Al_2O_3 aluminum oxide + SiH_4 silane

Balance the chemical equation algebraically: H_2 + Al + SiO_2 ⟶ Al_2O_3 + SiH_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 Al + c_3 SiO_2 ⟶ c_4 Al_2O_3 + c_5 SiH_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Al, O and Si: H: | 2 c_1 = 4 c_5 Al: | c_2 = 2 c_4 O: | 2 c_3 = 3 c_4 Si: | c_3 = c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3/2 c_4 = 1 c_5 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 4 c_3 = 3 c_4 = 2 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2 + 4 Al + 3 SiO_2 ⟶ 2 Al_2O_3 + 3 SiH_4

+ + ⟶ +

hydrogen + aluminum + silicon dioxide ⟶ aluminum oxide + silane

Construct the equilibrium constant, K, expression for: H_2 + Al + SiO_2 ⟶ Al_2O_3 + SiH_4 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: 6 H_2 + 4 Al + 3 SiO_2 ⟶ 2 Al_2O_3 + 3 SiH_4 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 | 6 | -6 Al | 4 | -4 SiO_2 | 3 | -3 Al_2O_3 | 2 | 2 SiH_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 6 | -6 | ([H2])^(-6) Al | 4 | -4 | ([Al])^(-4) SiO_2 | 3 | -3 | ([SiO2])^(-3) Al_2O_3 | 2 | 2 | ([Al2O3])^2 SiH_4 | 3 | 3 | ([SiH4])^3 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])^(-6) ([Al])^(-4) ([SiO2])^(-3) ([Al2O3])^2 ([SiH4])^3 = (([Al2O3])^2 ([SiH4])^3)/(([H2])^6 ([Al])^4 ([SiO2])^3)

Construct the rate of reaction expression for: H_2 + Al + SiO_2 ⟶ Al_2O_3 + SiH_4 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: 6 H_2 + 4 Al + 3 SiO_2 ⟶ 2 Al_2O_3 + 3 SiH_4 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 | 6 | -6 Al | 4 | -4 SiO_2 | 3 | -3 Al_2O_3 | 2 | 2 SiH_4 | 3 | 3 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 | 6 | -6 | -1/6 (Δ[H2])/(Δt) Al | 4 | -4 | -1/4 (Δ[Al])/(Δt) SiO_2 | 3 | -3 | -1/3 (Δ[SiO2])/(Δt) Al_2O_3 | 2 | 2 | 1/2 (Δ[Al2O3])/(Δt) SiH_4 | 3 | 3 | 1/3 (Δ[SiH4])/(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 = -1/6 (Δ[H2])/(Δt) = -1/4 (Δ[Al])/(Δt) = -1/3 (Δ[SiO2])/(Δt) = 1/2 (Δ[Al2O3])/(Δt) = 1/3 (Δ[SiH4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | aluminum | silicon dioxide | aluminum oxide | silane formula | H_2 | Al | SiO_2 | Al_2O_3 | SiH_4 Hill formula | H_2 | Al | O_2Si | Al_2O_3 | H_4Si name | hydrogen | aluminum | silicon dioxide | aluminum oxide | silane IUPAC name | molecular hydrogen | aluminum | dioxosilane | dialuminum;oxygen(2-) | silane

| hydrogen | aluminum | silicon dioxide | aluminum oxide | silane molar mass | 2.016 g/mol | 26.9815385 g/mol | 60.083 g/mol | 101.96 g/mol | 32.117 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) melting point | -259.2 °C | 660.4 °C | 1713 °C | 2040 °C | -185 °C boiling point | -252.8 °C | 2460 °C | 2950 °C | | -112 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.7 g/cm^3 | 2.196 g/cm^3 | | 0.001313 g/cm^3 (at 25 °C) solubility in water | | insoluble | 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 | odorless | odorless |