Au + H2SeO4 = H2O + SeO2 + Au2(SeO4)3

Au gold + H_2SeO_4 selenic acid ⟶ H_2O water + SeO_2 selenium dioxide + Au_2(SeO_4)_3 gold(III) selenate

Balance the chemical equation algebraically: Au + H_2SeO_4 ⟶ H_2O + SeO_2 + Au_2(SeO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Au + c_2 H_2SeO_4 ⟶ c_3 H_2O + c_4 SeO_2 + c_5 Au_2(SeO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Au, H, O and Se: Au: | c_1 = 2 c_5 H: | 2 c_2 = 2 c_3 O: | 4 c_2 = c_3 + 2 c_4 + 12 c_5 Se: | c_2 = c_4 + 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 6 c_3 = 6 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Au + 6 H_2SeO_4 ⟶ 6 H_2O + 3 SeO_2 + Au_2(SeO_4)_3

+ ⟶ + +

gold + selenic acid ⟶ water + selenium dioxide + gold(III) selenate

Construct the equilibrium constant, K, expression for: Au + H_2SeO_4 ⟶ H_2O + SeO_2 + Au_2(SeO_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 Au + 6 H_2SeO_4 ⟶ 6 H_2O + 3 SeO_2 + Au_2(SeO_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 Au | 2 | -2 H_2SeO_4 | 6 | -6 H_2O | 6 | 6 SeO_2 | 3 | 3 Au_2(SeO_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 Au | 2 | -2 | ([Au])^(-2) H_2SeO_4 | 6 | -6 | ([H2SeO4])^(-6) H_2O | 6 | 6 | ([H2O])^6 SeO_2 | 3 | 3 | ([SeO2])^3 Au_2(SeO_4)_3 | 1 | 1 | [Au2(SeO4)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 = ([Au])^(-2) ([H2SeO4])^(-6) ([H2O])^6 ([SeO2])^3 [Au2(SeO4)3] = (([H2O])^6 ([SeO2])^3 [Au2(SeO4)3])/(([Au])^2 ([H2SeO4])^6)

Construct the rate of reaction expression for: Au + H_2SeO_4 ⟶ H_2O + SeO_2 + Au_2(SeO_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 Au + 6 H_2SeO_4 ⟶ 6 H_2O + 3 SeO_2 + Au_2(SeO_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 Au | 2 | -2 H_2SeO_4 | 6 | -6 H_2O | 6 | 6 SeO_2 | 3 | 3 Au_2(SeO_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 Au | 2 | -2 | -1/2 (Δ[Au])/(Δt) H_2SeO_4 | 6 | -6 | -1/6 (Δ[H2SeO4])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) SeO_2 | 3 | 3 | 1/3 (Δ[SeO2])/(Δt) Au_2(SeO_4)_3 | 1 | 1 | (Δ[Au2(SeO4)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[Au])/(Δt) = -1/6 (Δ[H2SeO4])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[SeO2])/(Δt) = (Δ[Au2(SeO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| gold | selenic acid | water | selenium dioxide | gold(III) selenate formula | Au | H_2SeO_4 | H_2O | SeO_2 | Au_2(SeO_4)_3 Hill formula | Au | H_2O_4Se | H_2O | O_2Se | Au_2O_12Se_3 name | gold | selenic acid | water | selenium dioxide | gold(III) selenate