HCIO3 = H2O + CIO2 + HCIO4

HCIO3 ⟶ H_2O water + CIO2 + HCIO4

Balance the chemical equation algebraically: HCIO3 ⟶ H_2O + CIO2 + HCIO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCIO3 ⟶ c_2 H_2O + c_3 CIO2 + c_4 HCIO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, C, I and O: H: | c_1 = 2 c_2 + c_4 C: | c_1 = c_3 + c_4 I: | c_1 = c_3 + c_4 O: | 3 c_1 = c_2 + 2 c_3 + 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 HCIO3 ⟶ H_2O + 2 CIO2 + HCIO4

HCIO3 ⟶ + CIO2 + HCIO4

HCIO3 ⟶ water + CIO2 + HCIO4

Construct the equilibrium constant, K, expression for: HCIO3 ⟶ H_2O + CIO2 + HCIO4 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: 3 HCIO3 ⟶ H_2O + 2 CIO2 + HCIO4 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 HCIO3 | 3 | -3 H_2O | 1 | 1 CIO2 | 2 | 2 HCIO4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCIO3 | 3 | -3 | ([HCIO3])^(-3) H_2O | 1 | 1 | [H2O] CIO2 | 2 | 2 | ([CIO2])^2 HCIO4 | 1 | 1 | [HCIO4] 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 = ([HCIO3])^(-3) [H2O] ([CIO2])^2 [HCIO4] = ([H2O] ([CIO2])^2 [HCIO4])/([HCIO3])^3

Construct the rate of reaction expression for: HCIO3 ⟶ H_2O + CIO2 + HCIO4 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: 3 HCIO3 ⟶ H_2O + 2 CIO2 + HCIO4 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 HCIO3 | 3 | -3 H_2O | 1 | 1 CIO2 | 2 | 2 HCIO4 | 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 HCIO3 | 3 | -3 | -1/3 (Δ[HCIO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CIO2 | 2 | 2 | 1/2 (Δ[CIO2])/(Δt) HCIO4 | 1 | 1 | (Δ[HCIO4])/(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 = -1/3 (Δ[HCIO3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[CIO2])/(Δt) = (Δ[HCIO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| HCIO3 | water | CIO2 | HCIO4 formula | HCIO3 | H_2O | CIO2 | HCIO4 Hill formula | CHIO3 | H_2O | CIO2 | CHIO4 name | | water | |

| HCIO3 | water | CIO2 | HCIO4 molar mass | 187.92 g/mol | 18.015 g/mol | 170.913 g/mol | 203.92 g/mol phase | | liquid (at STP) | | melting point | | 0 °C | | boiling point | | 99.9839 °C | | density | | 1 g/cm^3 | | surface tension | | 0.0728 N/m | | dynamic viscosity | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | |