Al2(SO4)3 + Ba(NO3)2 = Al(NO3)3 + Ba(SO4)

Input interpretation

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Al_2(SO_4)_3 (aluminum sulfate) + Ba(NO_3)_2 (barium nitrate) ⟶ Al(NO_3)_3 (aluminum nitrate) + BaSO_4 (barium sulfate)

Balanced equation

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Balance the chemical equation algebraically: Al_2(SO_4)_3 + Ba(NO_3)_2 ⟶ Al(NO_3)_3 + BaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2(SO_4)_3 + c_2 Ba(NO_3)_2 ⟶ c_3 Al(NO_3)_3 + c_4 BaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O, S, Ba and N: Al: | 2 c_1 = c_3 O: | 12 c_1 + 6 c_2 = 9 c_3 + 4 c_4 S: | 3 c_1 = c_4 Ba: | c_2 = c_4 N: | 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al_2(SO_4)_3 + 3 Ba(NO_3)_2 ⟶ 2 Al(NO_3)_3 + 3 BaSO_4

+ ⟶ +

Names

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aluminum sulfate + barium nitrate ⟶ aluminum nitrate + barium sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Al_2(SO_4)_3 + Ba(NO_3)_2 ⟶ Al(NO_3)_3 + BaSO_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: Al_2(SO_4)_3 + 3 Ba(NO_3)_2 ⟶ 2 Al(NO_3)_3 + 3 BaSO_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 Al_2(SO_4)_3 | 1 | -1 Ba(NO_3)_2 | 3 | -3 Al(NO_3)_3 | 2 | 2 BaSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) Ba(NO_3)_2 | 3 | -3 | ([Ba(NO3)2])^(-3) Al(NO_3)_3 | 2 | 2 | ([Al(NO3)3])^2 BaSO_4 | 3 | 3 | ([BaSO4])^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 = ([Al2(SO4)3])^(-1) ([Ba(NO3)2])^(-3) ([Al(NO3)3])^2 ([BaSO4])^3 = (([Al(NO3)3])^2 ([BaSO4])^3)/([Al2(SO4)3] ([Ba(NO3)2])^3)

Rate of reaction

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Construct the rate of reaction expression for: Al_2(SO_4)_3 + Ba(NO_3)_2 ⟶ Al(NO_3)_3 + BaSO_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: Al_2(SO_4)_3 + 3 Ba(NO_3)_2 ⟶ 2 Al(NO_3)_3 + 3 BaSO_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 Al_2(SO_4)_3 | 1 | -1 Ba(NO_3)_2 | 3 | -3 Al(NO_3)_3 | 2 | 2 BaSO_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 Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) Ba(NO_3)_2 | 3 | -3 | -1/3 (Δ[Ba(NO3)2])/(Δt) Al(NO_3)_3 | 2 | 2 | 1/2 (Δ[Al(NO3)3])/(Δt) BaSO_4 | 3 | 3 | 1/3 (Δ[BaSO4])/(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 = -(Δ[Al2(SO4)3])/(Δt) = -1/3 (Δ[Ba(NO3)2])/(Δt) = 1/2 (Δ[Al(NO3)3])/(Δt) = 1/3 (Δ[BaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)