H2SO4 + Al = H2O + SO2 + Al(SO4)3

H_2SO_4 sulfuric acid + Al aluminum ⟶ H_2O water + SO_2 sulfur dioxide + Al(SO4)3

Balance the chemical equation algebraically: H_2SO_4 + Al ⟶ H_2O + SO_2 + Al(SO4)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Al ⟶ c_3 H_2O + c_4 SO_2 + c_5 Al(SO4)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Al: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = c_3 + 2 c_4 + 12 c_5 S: | c_1 = c_4 + 3 c_5 Al: | c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 6 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2SO_4 + Al ⟶ 6 H_2O + 3 SO_2 + Al(SO4)3

+ ⟶ + + Al(SO4)3

sulfuric acid + aluminum ⟶ water + sulfur dioxide + Al(SO4)3

Construct the equilibrium constant, K, expression for: H_2SO_4 + Al ⟶ H_2O + SO_2 + Al(SO4)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: 6 H_2SO_4 + Al ⟶ 6 H_2O + 3 SO_2 + Al(SO4)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 | 6 | -6 Al | 1 | -1 H_2O | 6 | 6 SO_2 | 3 | 3 Al(SO4)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 | 6 | -6 | ([H2SO4])^(-6) Al | 1 | -1 | ([Al])^(-1) H_2O | 6 | 6 | ([H2O])^6 SO_2 | 3 | 3 | ([SO2])^3 Al(SO4)3 | 1 | 1 | [Al(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])^(-6) ([Al])^(-1) ([H2O])^6 ([SO2])^3 [Al(SO4)3] = (([H2O])^6 ([SO2])^3 [Al(SO4)3])/(([H2SO4])^6 [Al])

Construct the rate of reaction expression for: H_2SO_4 + Al ⟶ H_2O + SO_2 + Al(SO4)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: 6 H_2SO_4 + Al ⟶ 6 H_2O + 3 SO_2 + Al(SO4)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 | 6 | -6 Al | 1 | -1 H_2O | 6 | 6 SO_2 | 3 | 3 Al(SO4)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 | 6 | -6 | -1/6 (Δ[H2SO4])/(Δt) Al | 1 | -1 | -(Δ[Al])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) Al(SO4)3 | 1 | 1 | (Δ[Al(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 = -1/6 (Δ[H2SO4])/(Δt) = -(Δ[Al])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[SO2])/(Δt) = (Δ[Al(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | aluminum | water | sulfur dioxide | Al(SO4)3 formula | H_2SO_4 | Al | H_2O | SO_2 | Al(SO4)3 Hill formula | H_2O_4S | Al | H_2O | O_2S | AlO12S3 name | sulfuric acid | aluminum | water | sulfur dioxide |