Al + KClO3 = KCl + Al2O3

Al aluminum + KClO_3 potassium chlorate ⟶ KCl potassium chloride + Al_2O_3 aluminum oxide

Balance the chemical equation algebraically: Al + KClO_3 ⟶ KCl + Al_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 KClO_3 ⟶ c_3 KCl + c_4 Al_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Cl, K and O: Al: | c_1 = 2 c_4 Cl: | c_2 = c_3 K: | c_2 = c_3 O: | 3 c_2 = 3 c_4 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + KClO_3 ⟶ KCl + Al_2O_3

+ ⟶ +

aluminum + potassium chlorate ⟶ potassium chloride + aluminum oxide

| aluminum | potassium chlorate | potassium chloride | aluminum oxide molecular enthalpy | 0 kJ/mol | -397.7 kJ/mol | -436.5 kJ/mol | -1676 kJ/mol total enthalpy | 0 kJ/mol | -397.7 kJ/mol | -436.5 kJ/mol | -1676 kJ/mol | H_initial = -397.7 kJ/mol | | H_final = -2113 kJ/mol | ΔH_rxn^0 | -2113 kJ/mol - -397.7 kJ/mol = -1715 kJ/mol (exothermic) | | |

| aluminum | potassium chlorate | potassium chloride | aluminum oxide molecular entropy | 28.3 J/(mol K) | 143 J/(mol K) | 83 J/(mol K) | 51 J/(mol K) total entropy | 56.6 J/(mol K) | 143 J/(mol K) | 83 J/(mol K) | 51 J/(mol K) | S_initial = 199.6 J/(mol K) | | S_final = 134 J/(mol K) | ΔS_rxn^0 | 134 J/(mol K) - 199.6 J/(mol K) = -65.6 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: Al + KClO_3 ⟶ KCl + 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: 2 Al + KClO_3 ⟶ KCl + 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 | 2 | -2 KClO_3 | 1 | -1 KCl | 1 | 1 Al_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 2 | -2 | ([Al])^(-2) KClO_3 | 1 | -1 | ([KClO3])^(-1) KCl | 1 | 1 | [KCl] Al_2O_3 | 1 | 1 | [Al2O3] 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])^(-2) ([KClO3])^(-1) [KCl] [Al2O3] = ([KCl] [Al2O3])/(([Al])^2 [KClO3])

Construct the rate of reaction expression for: Al + KClO_3 ⟶ KCl + 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: 2 Al + KClO_3 ⟶ KCl + 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 | 2 | -2 KClO_3 | 1 | -1 KCl | 1 | 1 Al_2O_3 | 1 | 1 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 | 2 | -2 | -1/2 (Δ[Al])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) Al_2O_3 | 1 | 1 | (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 = -1/2 (Δ[Al])/(Δt) = -(Δ[KClO3])/(Δt) = (Δ[KCl])/(Δt) = (Δ[Al2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | potassium chlorate | potassium chloride | aluminum oxide formula | Al | KClO_3 | KCl | Al_2O_3 Hill formula | Al | ClKO_3 | ClK | Al_2O_3 name | aluminum | potassium chlorate | potassium chloride | aluminum oxide IUPAC name | aluminum | potassium chlorate | potassium chloride | dialuminum;oxygen(2-)

| aluminum | potassium chlorate | potassium chloride | aluminum oxide molar mass | 26.9815385 g/mol | 122.5 g/mol | 74.55 g/mol | 101.96 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 660.4 °C | 356 °C | 770 °C | 2040 °C boiling point | 2460 °C | | 1420 °C | density | 2.7 g/cm^3 | 2.34 g/cm^3 | 1.98 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 | odorless