Mg + Al2(SO4)3 = Al + MgSO4

Input interpretation

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Mg magnesium + Al_2(SO_4)_3 aluminum sulfate ⟶ Al aluminum + MgSO_4 magnesium sulfate

Balanced equation

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Balance the chemical equation algebraically: Mg + Al_2(SO_4)_3 ⟶ Al + MgSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Al_2(SO_4)_3 ⟶ c_3 Al + c_4 MgSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Al, O and S: Mg: | c_1 = c_4 Al: | 2 c_2 = c_3 O: | 12 c_2 = 4 c_4 S: | 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 = 3 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Mg + Al_2(SO_4)_3 ⟶ 2 Al + 3 MgSO_4

+ ⟶ +

Names

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magnesium + aluminum sulfate ⟶ aluminum + magnesium sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Mg + Al_2(SO_4)_3 ⟶ Al + MgSO_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: 3 Mg + Al_2(SO_4)_3 ⟶ 2 Al + 3 MgSO_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 Mg | 3 | -3 Al_2(SO_4)_3 | 1 | -1 Al | 2 | 2 MgSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 3 | -3 | ([Mg])^(-3) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) Al | 2 | 2 | ([Al])^2 MgSO_4 | 3 | 3 | ([MgSO4])^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 = ([Mg])^(-3) ([Al2(SO4)3])^(-1) ([Al])^2 ([MgSO4])^3 = (([Al])^2 ([MgSO4])^3)/(([Mg])^3 [Al2(SO4)3])

Rate of reaction

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Construct the rate of reaction expression for: Mg + Al_2(SO_4)_3 ⟶ Al + MgSO_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: 3 Mg + Al_2(SO_4)_3 ⟶ 2 Al + 3 MgSO_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 Mg | 3 | -3 Al_2(SO_4)_3 | 1 | -1 Al | 2 | 2 MgSO_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 Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(Δt) MgSO_4 | 3 | 3 | 1/3 (Δ[MgSO4])/(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 = -1/3 (Δ[Mg])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = 1/2 (Δ[Al])/(Δt) = 1/3 (Δ[MgSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)