H2O + I2 + Na2SO3 = H2SO4 + NaI

H_2O water + I_2 iodine + Na_2SO_3 sodium sulfite ⟶ H_2SO_4 sulfuric acid + NaI sodium iodide

Balance the chemical equation algebraically: H_2O + I_2 + Na_2SO_3 ⟶ H_2SO_4 + NaI Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 I_2 + c_3 Na_2SO_3 ⟶ c_4 H_2SO_4 + c_5 NaI Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, I, Na and S: H: | 2 c_1 = 2 c_4 O: | c_1 + 3 c_3 = 4 c_4 I: | 2 c_2 = c_5 Na: | 2 c_3 = c_5 S: | c_3 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + I_2 + Na_2SO_3 ⟶ H_2SO_4 + 2 NaI

+ + ⟶ +

water + iodine + sodium sulfite ⟶ sulfuric acid + sodium iodide

| water | iodine | sodium sulfite | sulfuric acid | sodium iodide molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | -1101 kJ/mol | -814 kJ/mol | -287.8 kJ/mol total enthalpy | -285.8 kJ/mol | 0 kJ/mol | -1101 kJ/mol | -814 kJ/mol | -575.6 kJ/mol | H_initial = -1387 kJ/mol | | | H_final = -1390 kJ/mol | ΔH_rxn^0 | -1390 kJ/mol - -1387 kJ/mol = -2.97 kJ/mol (exothermic) | | | |

| water | iodine | sodium sulfite | sulfuric acid | sodium iodide molecular free energy | -237.1 kJ/mol | 0 kJ/mol | -10125 kJ/mol | -690 kJ/mol | -286.1 kJ/mol total free energy | -237.1 kJ/mol | 0 kJ/mol | -10125 kJ/mol | -690 kJ/mol | -572.2 kJ/mol | G_initial = -10362 kJ/mol | | | G_final = -1262 kJ/mol | ΔG_rxn^0 | -1262 kJ/mol - -10362 kJ/mol = 9100 kJ/mol (endergonic) | | | |

Construct the equilibrium constant, K, expression for: H_2O + I_2 + Na_2SO_3 ⟶ H_2SO_4 + NaI 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: H_2O + I_2 + Na_2SO_3 ⟶ H_2SO_4 + 2 NaI 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 | 1 | -1 I_2 | 1 | -1 Na_2SO_3 | 1 | -1 H_2SO_4 | 1 | 1 NaI | 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 | 1 | -1 | ([H2O])^(-1) I_2 | 1 | -1 | ([I2])^(-1) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] NaI | 2 | 2 | ([NaI])^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])^(-1) ([I2])^(-1) ([Na2SO3])^(-1) [H2SO4] ([NaI])^2 = ([H2SO4] ([NaI])^2)/([H2O] [I2] [Na2SO3])

Construct the rate of reaction expression for: H_2O + I_2 + Na_2SO_3 ⟶ H_2SO_4 + NaI 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: H_2O + I_2 + Na_2SO_3 ⟶ H_2SO_4 + 2 NaI 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 | 1 | -1 I_2 | 1 | -1 Na_2SO_3 | 1 | -1 H_2SO_4 | 1 | 1 NaI | 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 | 1 | -1 | -(Δ[H2O])/(Δt) I_2 | 1 | -1 | -(Δ[I2])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NaI | 2 | 2 | 1/2 (Δ[NaI])/(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 = -(Δ[H2O])/(Δt) = -(Δ[I2])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[H2SO4])/(Δt) = 1/2 (Δ[NaI])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | iodine | sodium sulfite | sulfuric acid | sodium iodide formula | H_2O | I_2 | Na_2SO_3 | H_2SO_4 | NaI Hill formula | H_2O | I_2 | Na_2O_3S | H_2O_4S | INa name | water | iodine | sodium sulfite | sulfuric acid | sodium iodide IUPAC name | water | molecular iodine | disodium sulfite | sulfuric acid | sodium iodide

| water | iodine | sodium sulfite | sulfuric acid | sodium iodide molar mass | 18.015 g/mol | 253.80894 g/mol | 126.04 g/mol | 98.07 g/mol | 149.89424 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | 0 °C | 113 °C | 500 °C | 10.371 °C | 661 °C boiling point | 99.9839 °C | 184 °C | | 279.6 °C | 1300 °C density | 1 g/cm^3 | 4.94 g/cm^3 | 2.63 g/cm^3 | 1.8305 g/cm^3 | 3.67 g/cm^3 solubility in water | | | | very soluble | surface tension | 0.0728 N/m | | | 0.0735 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.00227 Pa s (at 116 °C) | | 0.021 Pa s (at 25 °C) | 0.0010446 Pa s (at 691 °C) odor | odorless | | | odorless |