HNO3 + I2 = H2O + NO + HIO3

HNO_3 (nitric acid) + I_2 (iodine) ⟶ H_2O (water) + NO (nitric oxide) + HIO_3 (iodic acid)

Balance the chemical equation algebraically: HNO_3 + I_2 ⟶ H_2O + NO + HIO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 I_2 ⟶ c_3 H_2O + c_4 NO + c_5 HIO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and I: H: | c_1 = 2 c_3 + c_5 N: | c_1 = c_4 O: | 3 c_1 = c_3 + c_4 + 3 c_5 I: | 2 c_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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 3/2 c_3 = 1 c_4 = 5 c_5 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 10 c_2 = 3 c_3 = 2 c_4 = 10 c_5 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 3 I_2 ⟶ 2 H_2O + 10 NO + 6 HIO_3

+ ⟶ + +

nitric acid + iodine ⟶ water + nitric oxide + iodic acid

Construct the equilibrium constant, K, expression for: HNO_3 + I_2 ⟶ H_2O + NO + HIO_3 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: 10 HNO_3 + 3 I_2 ⟶ 2 H_2O + 10 NO + 6 HIO_3 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 HNO_3 | 10 | -10 I_2 | 3 | -3 H_2O | 2 | 2 NO | 10 | 10 HIO_3 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 10 | -10 | ([HNO3])^(-10) I_2 | 3 | -3 | ([I2])^(-3) H_2O | 2 | 2 | ([H2O])^2 NO | 10 | 10 | ([NO])^10 HIO_3 | 6 | 6 | ([HIO3])^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 = ([HNO3])^(-10) ([I2])^(-3) ([H2O])^2 ([NO])^10 ([HIO3])^6 = (([H2O])^2 ([NO])^10 ([HIO3])^6)/(([HNO3])^10 ([I2])^3)

Construct the rate of reaction expression for: HNO_3 + I_2 ⟶ H_2O + NO + HIO_3 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: 10 HNO_3 + 3 I_2 ⟶ 2 H_2O + 10 NO + 6 HIO_3 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 HNO_3 | 10 | -10 I_2 | 3 | -3 H_2O | 2 | 2 NO | 10 | 10 HIO_3 | 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 HNO_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) I_2 | 3 | -3 | -1/3 (Δ[I2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO | 10 | 10 | 1/10 (Δ[NO])/(Δt) HIO_3 | 6 | 6 | 1/6 (Δ[HIO3])/(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 = -1/10 (Δ[HNO3])/(Δt) = -1/3 (Δ[I2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/10 (Δ[NO])/(Δt) = 1/6 (Δ[HIO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | iodine | water | nitric oxide | iodic acid formula | HNO_3 | I_2 | H_2O | NO | HIO_3 name | nitric acid | iodine | water | nitric oxide | iodic acid IUPAC name | nitric acid | molecular iodine | water | nitric oxide | iodic acid