Al + H2SO3 = H2 + Al2(SO3)3

Input interpretation

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Al aluminum + H_2SO_3 sulfurous acid ⟶ H_2 hydrogen + Al2(SO3)3

Balanced equation

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Balance the chemical equation algebraically: Al + H_2SO_3 ⟶ H_2 + Al2(SO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 H_2SO_3 ⟶ c_3 H_2 + c_4 Al2(SO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, H, O and S: Al: | c_1 = 2 c_4 H: | 2 c_2 = 2 c_3 O: | 3 c_2 = 9 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 H_2SO_3 ⟶ 3 H_2 + Al2(SO3)3

+ ⟶ + Al2(SO3)3

Names

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aluminum + sulfurous acid ⟶ hydrogen + Al2(SO3)3

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Al + H_2SO_3 ⟶ H_2 + Al2(SO3)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 H_2SO_3 ⟶ 3 H_2 + Al2(SO3)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 H_2SO_3 | 3 | -3 H_2 | 3 | 3 Al2(SO3)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) H_2SO_3 | 3 | -3 | ([H2SO3])^(-3) H_2 | 3 | 3 | ([H2])^3 Al2(SO3)3 | 1 | 1 | [Al2(SO3)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) ([H2SO3])^(-3) ([H2])^3 [Al2(SO3)3] = (([H2])^3 [Al2(SO3)3])/(([Al])^2 ([H2SO3])^3)

Rate of reaction

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Construct the rate of reaction expression for: Al + H_2SO_3 ⟶ H_2 + Al2(SO3)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 H_2SO_3 ⟶ 3 H_2 + Al2(SO3)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 H_2SO_3 | 3 | -3 H_2 | 3 | 3 Al2(SO3)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) H_2SO_3 | 3 | -3 | -1/3 (Δ[H2SO3])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Al2(SO3)3 | 1 | 1 | (Δ[Al2(SO3)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[H2SO3])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[Al2(SO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)