Na + Al2(SO4)3 = Na2SO4 + Al

Na sodium + Al_2(SO_4)_3 aluminum sulfate ⟶ Na_2SO_4 sodium sulfate + Al aluminum

Balance the chemical equation algebraically: Na + Al_2(SO_4)_3 ⟶ Na_2SO_4 + Al Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 Al_2(SO_4)_3 ⟶ c_3 Na_2SO_4 + c_4 Al Set the number of atoms in the reactants equal to the number of atoms in the products for Na, Al, O and S: Na: | c_1 = 2 c_3 Al: | 2 c_2 = c_4 O: | 12 c_2 = 4 c_3 S: | 3 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 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Na + Al_2(SO_4)_3 ⟶ 3 Na_2SO_4 + 2 Al

+ ⟶ +

sodium + aluminum sulfate ⟶ sodium sulfate + aluminum

Construct the equilibrium constant, K, expression for: Na + Al_2(SO_4)_3 ⟶ Na_2SO_4 + Al 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_2(SO_4)_3 ⟶ 3 Na_2SO_4 + 2 Al 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_2(SO_4)_3 | 1 | -1 Na_2SO_4 | 3 | 3 Al | 2 | 2 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_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 Al | 2 | 2 | ([Al])^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 = ([Na])^(-6) ([Al2(SO4)3])^(-1) ([Na2SO4])^3 ([Al])^2 = (([Na2SO4])^3 ([Al])^2)/(([Na])^6 [Al2(SO4)3])

Construct the rate of reaction expression for: Na + Al_2(SO_4)_3 ⟶ Na_2SO_4 + Al 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_2(SO_4)_3 ⟶ 3 Na_2SO_4 + 2 Al 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_2(SO_4)_3 | 1 | -1 Na_2SO_4 | 3 | 3 Al | 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 Na | 6 | -6 | -1/6 (Δ[Na])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(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[Al2(SO4)3])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[Al])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | aluminum sulfate | sodium sulfate | aluminum formula | Na | Al_2(SO_4)_3 | Na_2SO_4 | Al Hill formula | Na | Al_2O_12S_3 | Na_2O_4S | Al name | sodium | aluminum sulfate | sodium sulfate | aluminum IUPAC name | sodium | dialuminum trisulfate | disodium sulfate | aluminum