Input interpretation
Na sodium + Al_2O_3 aluminum oxide ⟶ Al aluminum + Na_2O sodium oxide
Balanced equation
Balance the chemical equation algebraically: Na + Al_2O_3 ⟶ Al + Na_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 Al_2O_3 ⟶ c_3 Al + c_4 Na_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Na, Al and O: Na: | c_1 = 2 c_4 Al: | 2 c_2 = c_3 O: | 3 c_2 = 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 = 6 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Na + Al_2O_3 ⟶ 2 Al + 3 Na_2O
Structures
+ ⟶ +
Names
sodium + aluminum oxide ⟶ aluminum + sodium oxide
Equilibrium constant
![Construct the equilibrium constant, K, expression for: Na + Al_2O_3 ⟶ Al + Na_2O 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 Na + Al_2O_3 ⟶ 2 Al + 3 Na_2O 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 Na | 6 | -6 Al_2O_3 | 1 | -1 Al | 2 | 2 Na_2O | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 6 | -6 | ([Na])^(-6) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) Al | 2 | 2 | ([Al])^2 Na_2O | 3 | 3 | ([Na2O])^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 = ([Na])^(-6) ([Al2O3])^(-1) ([Al])^2 ([Na2O])^3 = (([Al])^2 ([Na2O])^3)/(([Na])^6 [Al2O3])](../image_source/56f333e3715481a778c3995d9cf2159a.png)
Construct the equilibrium constant, K, expression for: Na + Al_2O_3 ⟶ Al + Na_2O 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 Na + Al_2O_3 ⟶ 2 Al + 3 Na_2O 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 Na | 6 | -6 Al_2O_3 | 1 | -1 Al | 2 | 2 Na_2O | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 6 | -6 | ([Na])^(-6) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) Al | 2 | 2 | ([Al])^2 Na_2O | 3 | 3 | ([Na2O])^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 = ([Na])^(-6) ([Al2O3])^(-1) ([Al])^2 ([Na2O])^3 = (([Al])^2 ([Na2O])^3)/(([Na])^6 [Al2O3])
Rate of reaction
![Construct the rate of reaction expression for: Na + Al_2O_3 ⟶ Al + Na_2O 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 Na + Al_2O_3 ⟶ 2 Al + 3 Na_2O 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 Na | 6 | -6 Al_2O_3 | 1 | -1 Al | 2 | 2 Na_2O | 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 Na | 6 | -6 | -1/6 (Δ[Na])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(Δt) Na_2O | 3 | 3 | 1/3 (Δ[Na2O])/(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[Na])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/2 (Δ[Al])/(Δt) = 1/3 (Δ[Na2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/fcf7c6d974ff36639db05f9d4055ca7f.png)
Construct the rate of reaction expression for: Na + Al_2O_3 ⟶ Al + Na_2O 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 Na + Al_2O_3 ⟶ 2 Al + 3 Na_2O 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 Na | 6 | -6 Al_2O_3 | 1 | -1 Al | 2 | 2 Na_2O | 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 Na | 6 | -6 | -1/6 (Δ[Na])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(Δt) Na_2O | 3 | 3 | 1/3 (Δ[Na2O])/(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[Na])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/2 (Δ[Al])/(Δt) = 1/3 (Δ[Na2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sodium | aluminum oxide | aluminum | sodium oxide formula | Na | Al_2O_3 | Al | Na_2O name | sodium | aluminum oxide | aluminum | sodium oxide IUPAC name | sodium | dialuminum;oxygen(2-) | aluminum | disodium oxygen(-2) anion