Al + MgSO4 = Mg + Al2(SO4)3

Input interpretation

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

Balanced equation

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Balance the chemical equation algebraically: Al + MgSO_4 ⟶ Mg + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 MgSO_4 ⟶ c_3 Mg + c_4 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Mg, O and S: Al: | c_1 = 2 c_4 Mg: | c_2 = c_3 O: | 4 c_2 = 12 c_4 S: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 3 MgSO_4 ⟶ 3 Mg + Al_2(SO_4)_3

+ ⟶ +

Names

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aluminum + magnesium sulfate ⟶ magnesium + aluminum sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Al + MgSO_4 ⟶ Mg + Al_2(SO_4)_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 + 3 MgSO_4 ⟶ 3 Mg + Al_2(SO_4)_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 MgSO_4 | 3 | -3 Mg | 3 | 3 Al_2(SO_4)_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) MgSO_4 | 3 | -3 | ([MgSO4])^(-3) Mg | 3 | 3 | ([Mg])^3 Al_2(SO_4)_3 | 1 | 1 | [Al2(SO4)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 = ([Al])^(-2) ([MgSO4])^(-3) ([Mg])^3 [Al2(SO4)3] = (([Mg])^3 [Al2(SO4)3])/(([Al])^2 ([MgSO4])^3)

Rate of reaction

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