H2O + SO2 + HBrO3 = H2SO4 + HBr

H_2O water + SO_2 sulfur dioxide + HO_3Br bromic acid ⟶ H_2SO_4 sulfuric acid + HBr hydrogen bromide

Balance the chemical equation algebraically: H_2O + SO_2 + HO_3Br ⟶ H_2SO_4 + HBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 HO_3Br ⟶ c_4 H_2SO_4 + c_5 HBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Br: H: | 2 c_1 + c_3 = 2 c_4 + c_5 O: | c_1 + 2 c_2 + 3 c_3 = 4 c_4 S: | c_2 = c_4 Br: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 3 SO_2 + HO_3Br ⟶ 3 H_2SO_4 + HBr

+ + ⟶ +

water + sulfur dioxide + bromic acid ⟶ sulfuric acid + hydrogen bromide

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + HO_3Br ⟶ H_2SO_4 + HBr 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_2O + 3 SO_2 + HO_3Br ⟶ 3 H_2SO_4 + HBr 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_2O | 3 | -3 SO_2 | 3 | -3 HO_3Br | 1 | -1 H_2SO_4 | 3 | 3 HBr | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) SO_2 | 3 | -3 | ([SO2])^(-3) HO_3Br | 1 | -1 | ([H1O3Br1])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 HBr | 1 | 1 | [HBr] 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 = ([H2O])^(-3) ([SO2])^(-3) ([H1O3Br1])^(-1) ([H2SO4])^3 [HBr] = (([H2SO4])^3 [HBr])/(([H2O])^3 ([SO2])^3 [H1O3Br1])

Construct the rate of reaction expression for: H_2O + SO_2 + HO_3Br ⟶ H_2SO_4 + HBr 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_2O + 3 SO_2 + HO_3Br ⟶ 3 H_2SO_4 + HBr 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_2O | 3 | -3 SO_2 | 3 | -3 HO_3Br | 1 | -1 H_2SO_4 | 3 | 3 HBr | 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_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) SO_2 | 3 | -3 | -1/3 (Δ[SO2])/(Δt) HO_3Br | 1 | -1 | -(Δ[H1O3Br1])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) HBr | 1 | 1 | (Δ[HBr])/(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[H2O])/(Δt) = -1/3 (Δ[SO2])/(Δt) = -(Δ[H1O3Br1])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = (Δ[HBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | bromic acid | sulfuric acid | hydrogen bromide formula | H_2O | SO_2 | HO_3Br | H_2SO_4 | HBr Hill formula | H_2O | O_2S | BrHO_3 | H_2O_4S | BrH name | water | sulfur dioxide | bromic acid | sulfuric acid | hydrogen bromide