H2SO4 + Al + KClO = H2O + KCl + Al2(SO4)3

Input interpretation

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H_2SO_4 sulfuric acid + Al aluminum + KClO ⟶ H_2O water + KCl potassium chloride + Al_2(SO_4)_3 aluminum sulfate

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Al + KClO ⟶ H_2O + KCl + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Al + c_3 KClO ⟶ c_4 H_2O + c_5 KCl + c_6 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Al, K and Cl: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + c_3 = c_4 + 12 c_6 S: | c_1 = 3 c_6 Al: | c_2 = 2 c_6 K: | c_3 = c_5 Cl: | c_3 = c_5 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 Al + 3 KClO ⟶ 3 H_2O + 3 KCl + Al_2(SO_4)_3

+ + KClO ⟶ + +

Names

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sulfuric acid + aluminum + KClO ⟶ water + potassium chloride + aluminum sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Al + KClO ⟶ H_2O + KCl + 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: 3 H_2SO_4 + 2 Al + 3 KClO ⟶ 3 H_2O + 3 KCl + 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 H_2SO_4 | 3 | -3 Al | 2 | -2 KClO | 3 | -3 H_2O | 3 | 3 KCl | 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 H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) Al | 2 | -2 | ([Al])^(-2) KClO | 3 | -3 | ([KClO])^(-3) H_2O | 3 | 3 | ([H2O])^3 KCl | 3 | 3 | ([KCl])^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 = ([H2SO4])^(-3) ([Al])^(-2) ([KClO])^(-3) ([H2O])^3 ([KCl])^3 [Al2(SO4)3] = (([H2O])^3 ([KCl])^3 [Al2(SO4)3])/(([H2SO4])^3 ([Al])^2 ([KClO])^3)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Al + KClO ⟶ H_2O + KCl + 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: 3 H_2SO_4 + 2 Al + 3 KClO ⟶ 3 H_2O + 3 KCl + 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 H_2SO_4 | 3 | -3 Al | 2 | -2 KClO | 3 | -3 H_2O | 3 | 3 KCl | 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) KClO | 3 | -3 | -1/3 (Δ[KClO])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[Al])/(Δt) = -1/3 (Δ[KClO])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[KCl])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)