HCl + I2 + MnO2 = H2O + MnCl2 + HIO4

HCl hydrogen chloride + I_2 iodine + MnO_2 manganese dioxide ⟶ H_2O water + MnCl_2 manganese(II) chloride + HIO4

Balance the chemical equation algebraically: HCl + I_2 + MnO_2 ⟶ H_2O + MnCl_2 + HIO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 I_2 + c_3 MnO_2 ⟶ c_4 H_2O + c_5 MnCl_2 + c_6 HIO4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, I, Mn and O: Cl: | c_1 = 2 c_5 H: | c_1 = 2 c_4 + c_6 I: | 2 c_2 = c_6 Mn: | c_3 = c_5 O: | 2 c_3 = c_4 + 4 c_6 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 = 14 c_2 = 1 c_3 = 7 c_4 = 6 c_5 = 7 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + I_2 + 7 MnO_2 ⟶ 6 H_2O + 7 MnCl_2 + 2 HIO4

+ + ⟶ + + HIO4

hydrogen chloride + iodine + manganese dioxide ⟶ water + manganese(II) chloride + HIO4

Construct the equilibrium constant, K, expression for: HCl + I_2 + MnO_2 ⟶ H_2O + MnCl_2 + HIO4 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: 14 HCl + I_2 + 7 MnO_2 ⟶ 6 H_2O + 7 MnCl_2 + 2 HIO4 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 HCl | 14 | -14 I_2 | 1 | -1 MnO_2 | 7 | -7 H_2O | 6 | 6 MnCl_2 | 7 | 7 HIO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 14 | -14 | ([HCl])^(-14) I_2 | 1 | -1 | ([I2])^(-1) MnO_2 | 7 | -7 | ([MnO2])^(-7) H_2O | 6 | 6 | ([H2O])^6 MnCl_2 | 7 | 7 | ([MnCl2])^7 HIO4 | 2 | 2 | ([HIO4])^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 = ([HCl])^(-14) ([I2])^(-1) ([MnO2])^(-7) ([H2O])^6 ([MnCl2])^7 ([HIO4])^2 = (([H2O])^6 ([MnCl2])^7 ([HIO4])^2)/(([HCl])^14 [I2] ([MnO2])^7)

Construct the rate of reaction expression for: HCl + I_2 + MnO_2 ⟶ H_2O + MnCl_2 + HIO4 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: 14 HCl + I_2 + 7 MnO_2 ⟶ 6 H_2O + 7 MnCl_2 + 2 HIO4 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 HCl | 14 | -14 I_2 | 1 | -1 MnO_2 | 7 | -7 H_2O | 6 | 6 MnCl_2 | 7 | 7 HIO4 | 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 HCl | 14 | -14 | -1/14 (Δ[HCl])/(Δt) I_2 | 1 | -1 | -(Δ[I2])/(Δt) MnO_2 | 7 | -7 | -1/7 (Δ[MnO2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) MnCl_2 | 7 | 7 | 1/7 (Δ[MnCl2])/(Δt) HIO4 | 2 | 2 | 1/2 (Δ[HIO4])/(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 = -1/14 (Δ[HCl])/(Δt) = -(Δ[I2])/(Δt) = -1/7 (Δ[MnO2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/7 (Δ[MnCl2])/(Δt) = 1/2 (Δ[HIO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | iodine | manganese dioxide | water | manganese(II) chloride | HIO4 formula | HCl | I_2 | MnO_2 | H_2O | MnCl_2 | HIO4 Hill formula | ClH | I_2 | MnO_2 | H_2O | Cl_2Mn | HIO4 name | hydrogen chloride | iodine | manganese dioxide | water | manganese(II) chloride | IUPAC name | hydrogen chloride | molecular iodine | dioxomanganese | water | dichloromanganese |

| hydrogen chloride | iodine | manganese dioxide | water | manganese(II) chloride | HIO4 molar mass | 36.46 g/mol | 253.80894 g/mol | 86.936 g/mol | 18.015 g/mol | 125.8 g/mol | 191.91 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | melting point | -114.17 °C | 113 °C | 535 °C | 0 °C | 652 °C | boiling point | -85 °C | 184 °C | | 99.9839 °C | | density | 0.00149 g/cm^3 (at 25 °C) | 4.94 g/cm^3 | 5.03 g/cm^3 | 1 g/cm^3 | 2.98 g/cm^3 | solubility in water | miscible | | insoluble | | | surface tension | | | | 0.0728 N/m | | dynamic viscosity | | 0.00227 Pa s (at 116 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | |