H2O + SO2 + NaIO3 = H2SO4 + I2 + NaHSO4

H_2O water + SO_2 sulfur dioxide + NaIO_3 sodium iodate ⟶ H_2SO_4 sulfuric acid + I_2 iodine + NaHSO_4 sodium bisulfate

Balance the chemical equation algebraically: H_2O + SO_2 + NaIO_3 ⟶ H_2SO_4 + I_2 + NaHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 NaIO_3 ⟶ c_4 H_2SO_4 + c_5 I_2 + c_6 NaHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, I and Na: H: | 2 c_1 = 2 c_4 + c_6 O: | c_1 + 2 c_2 + 3 c_3 = 4 c_4 + 4 c_6 S: | c_2 = c_4 + c_6 I: | c_3 = 2 c_5 Na: | c_3 = c_6 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 = 3 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 5 SO_2 + 2 NaIO_3 ⟶ 3 H_2SO_4 + I_2 + 2 NaHSO_4

+ + ⟶ + +

water + sulfur dioxide + sodium iodate ⟶ sulfuric acid + iodine + sodium bisulfate

| water | sulfur dioxide | sodium iodate | sulfuric acid | iodine | sodium bisulfate molecular enthalpy | -285.8 kJ/mol | -296.8 kJ/mol | -481.8 kJ/mol | -814 kJ/mol | 0 kJ/mol | -1126 kJ/mol total enthalpy | -1143 kJ/mol | -1484 kJ/mol | -963.6 kJ/mol | -2442 kJ/mol | 0 kJ/mol | -2251 kJ/mol | H_initial = -3591 kJ/mol | | | H_final = -4693 kJ/mol | | ΔH_rxn^0 | -4693 kJ/mol - -3591 kJ/mol = -1102 kJ/mol (exothermic) | | | | |

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + NaIO_3 ⟶ H_2SO_4 + I_2 + NaHSO_4 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 NaIO_3 ⟶ 3 H_2SO_4 + I_2 + 2 NaHSO_4 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 NaIO_3 | 2 | -2 H_2SO_4 | 3 | 3 I_2 | 1 | 1 NaHSO_4 | 2 | 2 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) NaIO_3 | 2 | -2 | ([NaIO3])^(-2) H_2SO_4 | 3 | 3 | ([H2SO4])^3 I_2 | 1 | 1 | [I2] NaHSO_4 | 2 | 2 | ([NaHSO4])^2 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) ([NaIO3])^(-2) ([H2SO4])^3 [I2] ([NaHSO4])^2 = (([H2SO4])^3 [I2] ([NaHSO4])^2)/(([H2O])^4 ([SO2])^5 ([NaIO3])^2)

Construct the rate of reaction expression for: H_2O + SO_2 + NaIO_3 ⟶ H_2SO_4 + I_2 + NaHSO_4 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 NaIO_3 ⟶ 3 H_2SO_4 + I_2 + 2 NaHSO_4 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 NaIO_3 | 2 | -2 H_2SO_4 | 3 | 3 I_2 | 1 | 1 NaHSO_4 | 2 | 2 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) NaIO_3 | 2 | -2 | -1/2 (Δ[NaIO3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) I_2 | 1 | 1 | (Δ[I2])/(Δt) NaHSO_4 | 2 | 2 | 1/2 (Δ[NaHSO4])/(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[NaIO3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = (Δ[I2])/(Δt) = 1/2 (Δ[NaHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | sodium iodate | sulfuric acid | iodine | sodium bisulfate formula | H_2O | SO_2 | NaIO_3 | H_2SO_4 | I_2 | NaHSO_4 Hill formula | H_2O | O_2S | INaO_3 | H_2O_4S | I_2 | HNaO_4S name | water | sulfur dioxide | sodium iodate | sulfuric acid | iodine | sodium bisulfate IUPAC name | water | sulfur dioxide | sodium iodate | sulfuric acid | molecular iodine |