H2O + SO2 + HIO3 = H2SO4 + HI

H_2O water + SO_2 sulfur dioxide + HIO_3 iodic acid ⟶ H_2SO_4 sulfuric acid + HI hydrogen iodide

Balance the chemical equation algebraically: H_2O + SO_2 + HIO_3 ⟶ H_2SO_4 + HI Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 HIO_3 ⟶ c_4 H_2SO_4 + c_5 HI Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and I: 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 I: | 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 + HIO_3 ⟶ 3 H_2SO_4 + HI

+ + ⟶ +

water + sulfur dioxide + iodic acid ⟶ sulfuric acid + hydrogen iodide

| water | sulfur dioxide | iodic acid | sulfuric acid | hydrogen iodide molecular enthalpy | -285.8 kJ/mol | -296.8 kJ/mol | -230.1 kJ/mol | -814 kJ/mol | 26.5 kJ/mol total enthalpy | -857.5 kJ/mol | -890.4 kJ/mol | -230.1 kJ/mol | -2442 kJ/mol | 26.5 kJ/mol | H_initial = -1978 kJ/mol | | | H_final = -2416 kJ/mol | ΔH_rxn^0 | -2416 kJ/mol - -1978 kJ/mol = -437.5 kJ/mol (exothermic) | | | |

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + HIO_3 ⟶ H_2SO_4 + HI 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 + HIO_3 ⟶ 3 H_2SO_4 + HI 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 HIO_3 | 1 | -1 H_2SO_4 | 3 | 3 HI | 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) HIO_3 | 1 | -1 | ([HIO3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 HI | 1 | 1 | [HI] 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) ([HIO3])^(-1) ([H2SO4])^3 [HI] = (([H2SO4])^3 [HI])/(([H2O])^3 ([SO2])^3 [HIO3])

Construct the rate of reaction expression for: H_2O + SO_2 + HIO_3 ⟶ H_2SO_4 + HI 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 + HIO_3 ⟶ 3 H_2SO_4 + HI 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 HIO_3 | 1 | -1 H_2SO_4 | 3 | 3 HI | 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) HIO_3 | 1 | -1 | -(Δ[HIO3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) HI | 1 | 1 | (Δ[HI])/(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[HIO3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = (Δ[HI])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | iodic acid | sulfuric acid | hydrogen iodide formula | H_2O | SO_2 | HIO_3 | H_2SO_4 | HI Hill formula | H_2O | O_2S | HIO_3 | H_2O_4S | HI name | water | sulfur dioxide | iodic acid | sulfuric acid | hydrogen iodide