H2O + SO2 + HBrO3 = H2SO4 + Br2

H_2O water + SO_2 sulfur dioxide + HO_3Br bromic acid ⟶ H_2SO_4 sulfuric acid + Br_2 bromine

Balance the chemical equation algebraically: H_2O + SO_2 + HO_3Br ⟶ H_2SO_4 + Br_2 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 Br_2 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 O: | c_1 + 2 c_2 + 3 c_3 = 4 c_4 S: | c_2 = c_4 Br: | c_3 = 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 = 4 c_2 = 5 c_3 = 2 c_4 = 5 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 5 SO_2 + 2 HO_3Br ⟶ 5 H_2SO_4 + Br_2

+ + ⟶ +

water + sulfur dioxide + bromic acid ⟶ sulfuric acid + bromine

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + HO_3Br ⟶ H_2SO_4 + Br_2 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: 4 H_2O + 5 SO_2 + 2 HO_3Br ⟶ 5 H_2SO_4 + Br_2 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 | 4 | -4 SO_2 | 5 | -5 HO_3Br | 2 | -2 H_2SO_4 | 5 | 5 Br_2 | 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 | 4 | -4 | ([H2O])^(-4) SO_2 | 5 | -5 | ([SO2])^(-5) HO_3Br | 2 | -2 | ([H1O3Br1])^(-2) H_2SO_4 | 5 | 5 | ([H2SO4])^5 Br_2 | 1 | 1 | [Br2] 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])^(-4) ([SO2])^(-5) ([H1O3Br1])^(-2) ([H2SO4])^5 [Br2] = (([H2SO4])^5 [Br2])/(([H2O])^4 ([SO2])^5 ([H1O3Br1])^2)

Construct the rate of reaction expression for: H_2O + SO_2 + HO_3Br ⟶ H_2SO_4 + Br_2 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: 4 H_2O + 5 SO_2 + 2 HO_3Br ⟶ 5 H_2SO_4 + Br_2 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 | 4 | -4 SO_2 | 5 | -5 HO_3Br | 2 | -2 H_2SO_4 | 5 | 5 Br_2 | 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 | 4 | -4 | -1/4 (Δ[H2O])/(Δt) SO_2 | 5 | -5 | -1/5 (Δ[SO2])/(Δt) HO_3Br | 2 | -2 | -1/2 (Δ[H1O3Br1])/(Δt) H_2SO_4 | 5 | 5 | 1/5 (Δ[H2SO4])/(Δt) Br_2 | 1 | 1 | (Δ[Br2])/(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 = -1/4 (Δ[H2O])/(Δt) = -1/5 (Δ[SO2])/(Δt) = -1/2 (Δ[H1O3Br1])/(Δt) = 1/5 (Δ[H2SO4])/(Δt) = (Δ[Br2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | bromic acid | sulfuric acid | bromine formula | H_2O | SO_2 | HO_3Br | H_2SO_4 | Br_2 Hill formula | H_2O | O_2S | BrHO_3 | H_2O_4S | Br_2 name | water | sulfur dioxide | bromic acid | sulfuric acid | bromine IUPAC name | water | sulfur dioxide | bromic acid | sulfuric acid | molecular bromine