MnO2 + HI = H2O + I2 + MnI2

MnO_2 manganese dioxide + HI hydrogen iodide ⟶ H_2O water + I_2 iodine + MnI_2 manganese(II) iodide

Balance the chemical equation algebraically: MnO_2 + HI ⟶ H_2O + I_2 + MnI_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 HI ⟶ c_3 H_2O + c_4 I_2 + c_5 MnI_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, H and I: Mn: | c_1 = c_5 O: | 2 c_1 = c_3 H: | c_2 = 2 c_3 I: | c_2 = 2 c_4 + 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 = 4 c_3 = 2 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnO_2 + 4 HI ⟶ 2 H_2O + I_2 + MnI_2

+ ⟶ + +

manganese dioxide + hydrogen iodide ⟶ water + iodine + manganese(II) iodide

Construct the equilibrium constant, K, expression for: MnO_2 + HI ⟶ H_2O + I_2 + MnI_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: MnO_2 + 4 HI ⟶ 2 H_2O + I_2 + MnI_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 MnO_2 | 1 | -1 HI | 4 | -4 H_2O | 2 | 2 I_2 | 1 | 1 MnI_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 1 | -1 | ([MnO2])^(-1) HI | 4 | -4 | ([HI])^(-4) H_2O | 2 | 2 | ([H2O])^2 I_2 | 1 | 1 | [I2] MnI_2 | 1 | 1 | [MnI2] 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 = ([MnO2])^(-1) ([HI])^(-4) ([H2O])^2 [I2] [MnI2] = (([H2O])^2 [I2] [MnI2])/([MnO2] ([HI])^4)

Construct the rate of reaction expression for: MnO_2 + HI ⟶ H_2O + I_2 + MnI_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: MnO_2 + 4 HI ⟶ 2 H_2O + I_2 + MnI_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 MnO_2 | 1 | -1 HI | 4 | -4 H_2O | 2 | 2 I_2 | 1 | 1 MnI_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 MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) HI | 4 | -4 | -1/4 (Δ[HI])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) I_2 | 1 | 1 | (Δ[I2])/(Δt) MnI_2 | 1 | 1 | (Δ[MnI2])/(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[MnO2])/(Δt) = -1/4 (Δ[HI])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[I2])/(Δt) = (Δ[MnI2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese dioxide | hydrogen iodide | water | iodine | manganese(II) iodide formula | MnO_2 | HI | H_2O | I_2 | MnI_2 Hill formula | MnO_2 | HI | H_2O | I_2 | I_2Mn name | manganese dioxide | hydrogen iodide | water | iodine | manganese(II) iodide IUPAC name | dioxomanganese | hydrogen iodide | water | molecular iodine | manganous diiodide

| manganese dioxide | hydrogen iodide | water | iodine | manganese(II) iodide molar mass | 86.936 g/mol | 127.912 g/mol | 18.015 g/mol | 253.80894 g/mol | 308.74698 g/mol phase | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 535 °C | -50.76 °C | 0 °C | 113 °C | 80 °C boiling point | | -35.55 °C | 99.9839 °C | 184 °C | density | 5.03 g/cm^3 | 0.005228 g/cm^3 (at 25 °C) | 1 g/cm^3 | 4.94 g/cm^3 | 5.01 g/cm^3 solubility in water | insoluble | very soluble | | | soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | 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 | |