H2SO4 + HI + KIO3 = H2O + K2SO4 + I2

H_2SO_4 sulfuric acid + HI hydrogen iodide + KIO_3 potassium iodate ⟶ H_2O water + K_2SO_4 potassium sulfate + I_2 iodine

Balance the chemical equation algebraically: H_2SO_4 + HI + KIO_3 ⟶ H_2O + K_2SO_4 + I_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 HI + c_3 KIO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 I_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, I and K: H: | 2 c_1 + c_2 = 2 c_4 O: | 4 c_1 + 3 c_3 = c_4 + 4 c_5 S: | c_1 = c_5 I: | c_2 + c_3 = 2 c_6 K: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 10 c_3 = 2 c_4 = 6 c_5 = 1 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 10 HI + 2 KIO_3 ⟶ 6 H_2O + K_2SO_4 + 6 I_2

+ + ⟶ + +

sulfuric acid + hydrogen iodide + potassium iodate ⟶ water + potassium sulfate + iodine

Construct the equilibrium constant, K, expression for: H_2SO_4 + HI + KIO_3 ⟶ H_2O + K_2SO_4 + I_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: H_2SO_4 + 10 HI + 2 KIO_3 ⟶ 6 H_2O + K_2SO_4 + 6 I_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_2SO_4 | 1 | -1 HI | 10 | -10 KIO_3 | 2 | -2 H_2O | 6 | 6 K_2SO_4 | 1 | 1 I_2 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) HI | 10 | -10 | ([HI])^(-10) KIO_3 | 2 | -2 | ([KIO3])^(-2) H_2O | 6 | 6 | ([H2O])^6 K_2SO_4 | 1 | 1 | [K2SO4] I_2 | 6 | 6 | ([I2])^6 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 = ([H2SO4])^(-1) ([HI])^(-10) ([KIO3])^(-2) ([H2O])^6 [K2SO4] ([I2])^6 = (([H2O])^6 [K2SO4] ([I2])^6)/([H2SO4] ([HI])^10 ([KIO3])^2)

Construct the rate of reaction expression for: H_2SO_4 + HI + KIO_3 ⟶ H_2O + K_2SO_4 + I_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: H_2SO_4 + 10 HI + 2 KIO_3 ⟶ 6 H_2O + K_2SO_4 + 6 I_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_2SO_4 | 1 | -1 HI | 10 | -10 KIO_3 | 2 | -2 H_2O | 6 | 6 K_2SO_4 | 1 | 1 I_2 | 6 | 6 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_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) HI | 10 | -10 | -1/10 (Δ[HI])/(Δt) KIO_3 | 2 | -2 | -1/2 (Δ[KIO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) I_2 | 6 | 6 | 1/6 (Δ[I2])/(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[H2SO4])/(Δt) = -1/10 (Δ[HI])/(Δt) = -1/2 (Δ[KIO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/6 (Δ[I2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | hydrogen iodide | potassium iodate | water | potassium sulfate | iodine formula | H_2SO_4 | HI | KIO_3 | H_2O | K_2SO_4 | I_2 Hill formula | H_2O_4S | HI | IKO_3 | H_2O | K_2O_4S | I_2 name | sulfuric acid | hydrogen iodide | potassium iodate | water | potassium sulfate | iodine IUPAC name | sulfuric acid | hydrogen iodide | potassium iodate | water | dipotassium sulfate | molecular iodine

| sulfuric acid | hydrogen iodide | potassium iodate | water | potassium sulfate | iodine molar mass | 98.07 g/mol | 127.912 g/mol | 214 g/mol | 18.015 g/mol | 174.25 g/mol | 253.80894 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) melting point | 10.371 °C | -50.76 °C | 560 °C | 0 °C | | 113 °C boiling point | 279.6 °C | -35.55 °C | | 99.9839 °C | | 184 °C density | 1.8305 g/cm^3 | 0.005228 g/cm^3 (at 25 °C) | 1.005 g/cm^3 | 1 g/cm^3 | | 4.94 g/cm^3 solubility in water | very soluble | very soluble | | | soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 0.001321 Pa s (at -39 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 0.00227 Pa s (at 116 °C) odor | odorless | | | odorless | |