Al + NH4ClO4 = Al2O3 + NH4Cl

Al aluminum + NH_4ClO_4 ammonium perchlorate ⟶ Al_2O_3 aluminum oxide + NH_4Cl ammonium chloride

Balance the chemical equation algebraically: Al + NH_4ClO_4 ⟶ Al_2O_3 + NH_4Cl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 NH_4ClO_4 ⟶ c_3 Al_2O_3 + c_4 NH_4Cl Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Cl, H, N and O: Al: | c_1 = 2 c_3 Cl: | c_2 = c_4 H: | 4 c_2 = 4 c_4 N: | c_2 = c_4 O: | 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8/3 c_2 = 1 c_3 = 4/3 c_4 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 8 c_2 = 3 c_3 = 4 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 Al + 3 NH_4ClO_4 ⟶ 4 Al_2O_3 + 3 NH_4Cl

+ ⟶ +

aluminum + ammonium perchlorate ⟶ aluminum oxide + ammonium chloride

Construct the equilibrium constant, K, expression for: Al + NH_4ClO_4 ⟶ Al_2O_3 + NH_4Cl 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: 8 Al + 3 NH_4ClO_4 ⟶ 4 Al_2O_3 + 3 NH_4Cl 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 | 8 | -8 NH_4ClO_4 | 3 | -3 Al_2O_3 | 4 | 4 NH_4Cl | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 8 | -8 | ([Al])^(-8) NH_4ClO_4 | 3 | -3 | ([NH4ClO4])^(-3) Al_2O_3 | 4 | 4 | ([Al2O3])^4 NH_4Cl | 3 | 3 | ([NH4Cl])^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 = ([Al])^(-8) ([NH4ClO4])^(-3) ([Al2O3])^4 ([NH4Cl])^3 = (([Al2O3])^4 ([NH4Cl])^3)/(([Al])^8 ([NH4ClO4])^3)

Construct the rate of reaction expression for: Al + NH_4ClO_4 ⟶ Al_2O_3 + NH_4Cl 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: 8 Al + 3 NH_4ClO_4 ⟶ 4 Al_2O_3 + 3 NH_4Cl 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 | 8 | -8 NH_4ClO_4 | 3 | -3 Al_2O_3 | 4 | 4 NH_4Cl | 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 Al | 8 | -8 | -1/8 (Δ[Al])/(Δt) NH_4ClO_4 | 3 | -3 | -1/3 (Δ[NH4ClO4])/(Δt) Al_2O_3 | 4 | 4 | 1/4 (Δ[Al2O3])/(Δt) NH_4Cl | 3 | 3 | 1/3 (Δ[NH4Cl])/(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 = -1/8 (Δ[Al])/(Δt) = -1/3 (Δ[NH4ClO4])/(Δt) = 1/4 (Δ[Al2O3])/(Δt) = 1/3 (Δ[NH4Cl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | ammonium perchlorate | aluminum oxide | ammonium chloride formula | Al | NH_4ClO_4 | Al_2O_3 | NH_4Cl Hill formula | Al | ClH_4NO_4 | Al_2O_3 | ClH_4N name | aluminum | ammonium perchlorate | aluminum oxide | ammonium chloride IUPAC name | aluminum | | dialuminum;oxygen(2-) | ammonium chloride

| aluminum | ammonium perchlorate | aluminum oxide | ammonium chloride molar mass | 26.9815385 g/mol | 117.5 g/mol | 101.96 g/mol | 53.49 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 660.4 °C | | 2040 °C | 340 °C boiling point | 2460 °C | | | density | 2.7 g/cm^3 | 1.95 g/cm^3 | | 1.5256 g/cm^3 solubility in water | insoluble | soluble | | soluble surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | | odor | odorless | | odorless |