H2SO4 + Ti = H2O + SO2 + Ti2(SO4)3

H_2SO_4 sulfuric acid + Ti titanium ⟶ H_2O water + SO_2 sulfur dioxide + Ti_2(SO_4)_3 titanium(III) sulfate

Balance the chemical equation algebraically: H_2SO_4 + Ti ⟶ H_2O + SO_2 + Ti_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Ti ⟶ c_3 H_2O + c_4 SO_2 + c_5 Ti_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 and Ti: 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 Ti: | c_2 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 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 + 2 Ti ⟶ 6 H_2O + 3 SO_2 + Ti_2(SO_4)_3

+ ⟶ + +

sulfuric acid + titanium ⟶ water + sulfur dioxide + titanium(III) sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + Ti ⟶ H_2O + SO_2 + Ti_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: 6 H_2SO_4 + 2 Ti ⟶ 6 H_2O + 3 SO_2 + Ti_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 | 6 | -6 Ti | 2 | -2 H_2O | 6 | 6 SO_2 | 3 | 3 Ti_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 | 6 | -6 | ([H2SO4])^(-6) Ti | 2 | -2 | ([Ti])^(-2) H_2O | 6 | 6 | ([H2O])^6 SO_2 | 3 | 3 | ([SO2])^3 Ti_2(SO_4)_3 | 1 | 1 | [Ti2(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) ([Ti])^(-2) ([H2O])^6 ([SO2])^3 [Ti2(SO4)3] = (([H2O])^6 ([SO2])^3 [Ti2(SO4)3])/(([H2SO4])^6 ([Ti])^2)

Construct the rate of reaction expression for: H_2SO_4 + Ti ⟶ H_2O + SO_2 + Ti_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: 6 H_2SO_4 + 2 Ti ⟶ 6 H_2O + 3 SO_2 + Ti_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 | 6 | -6 Ti | 2 | -2 H_2O | 6 | 6 SO_2 | 3 | 3 Ti_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 | 6 | -6 | -1/6 (Δ[H2SO4])/(Δt) Ti | 2 | -2 | -1/2 (Δ[Ti])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) Ti_2(SO_4)_3 | 1 | 1 | (Δ[Ti2(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) = -1/2 (Δ[Ti])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[SO2])/(Δt) = (Δ[Ti2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | titanium | water | sulfur dioxide | titanium(III) sulfate formula | H_2SO_4 | Ti | H_2O | SO_2 | Ti_2(SO_4)_3 Hill formula | H_2O_4S | Ti | H_2O | O_2S | O_12S_3Ti_2 name | sulfuric acid | titanium | water | sulfur dioxide | titanium(III) sulfate IUPAC name | sulfuric acid | titanium | water | sulfur dioxide | titanium(+3) cation trisulfate