HIO3 + H2SO3 = H2O + H2SO4 + I2

Input interpretation

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HIO_3 iodic acid + H_2SO_3 sulfurous acid ⟶ H_2O water + H_2SO_4 sulfuric acid + I_2 iodine

Balanced equation

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Balance the chemical equation algebraically: HIO_3 + H_2SO_3 ⟶ H_2O + H_2SO_4 + I_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HIO_3 + c_2 H_2SO_3 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 I_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, I, O and S: H: | c_1 + 2 c_2 = 2 c_3 + 2 c_4 I: | c_1 = 2 c_5 O: | 3 c_1 + 3 c_2 = c_3 + 4 c_4 S: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 5 c_3 = 1 c_4 = 5 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HIO_3 + 5 H_2SO_3 ⟶ H_2O + 5 H_2SO_4 + I_2

+ ⟶ + +

Names

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iodic acid + sulfurous acid ⟶ water + sulfuric acid + iodine

Equilibrium constant

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Construct the equilibrium constant, K, expression for: HIO_3 + H_2SO_3 ⟶ H_2O + H_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: 2 HIO_3 + 5 H_2SO_3 ⟶ H_2O + 5 H_2SO_4 + 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 HIO_3 | 2 | -2 H_2SO_3 | 5 | -5 H_2O | 1 | 1 H_2SO_4 | 5 | 5 I_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HIO_3 | 2 | -2 | ([HIO3])^(-2) H_2SO_3 | 5 | -5 | ([H2SO3])^(-5) H_2O | 1 | 1 | [H2O] H_2SO_4 | 5 | 5 | ([H2SO4])^5 I_2 | 1 | 1 | [I2] 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 = ([HIO3])^(-2) ([H2SO3])^(-5) [H2O] ([H2SO4])^5 [I2] = ([H2O] ([H2SO4])^5 [I2])/(([HIO3])^2 ([H2SO3])^5)

Rate of reaction

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Construct the rate of reaction expression for: HIO_3 + H_2SO_3 ⟶ H_2O + H_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: 2 HIO_3 + 5 H_2SO_3 ⟶ H_2O + 5 H_2SO_4 + 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 HIO_3 | 2 | -2 H_2SO_3 | 5 | -5 H_2O | 1 | 1 H_2SO_4 | 5 | 5 I_2 | 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 HIO_3 | 2 | -2 | -1/2 (Δ[HIO3])/(Δt) H_2SO_3 | 5 | -5 | -1/5 (Δ[H2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) H_2SO_4 | 5 | 5 | 1/5 (Δ[H2SO4])/(Δt) I_2 | 1 | 1 | (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 = -1/2 (Δ[HIO3])/(Δt) = -1/5 (Δ[H2SO3])/(Δt) = (Δ[H2O])/(Δt) = 1/5 (Δ[H2SO4])/(Δt) = (Δ[I2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)