H2SO4 + MnO2 + KI = H2O + I2 + MnSO4 + KHSO4

H_2SO_4 (sulfuric acid) + MnO_2 (manganese dioxide) + KI (potassium iodide) ⟶ H_2O (water) + I_2 (iodine) + MnSO_4 (manganese(II) sulfate) + KHSO_4 (potassium bisulfate)

Balance the chemical equation algebraically: H_2SO_4 + MnO_2 + KI ⟶ H_2O + I_2 + MnSO_4 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 MnO_2 + c_3 KI ⟶ c_4 H_2O + c_5 I_2 + c_6 MnSO_4 + c_7 KHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Mn, I and K: H: | 2 c_1 = 2 c_4 + c_7 O: | 4 c_1 + 2 c_2 = c_4 + 4 c_6 + 4 c_7 S: | c_1 = c_6 + c_7 Mn: | c_2 = c_6 I: | c_3 = 2 c_5 K: | c_3 = c_7 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 = 2 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + MnO_2 + 2 KI ⟶ 2 H_2O + I_2 + MnSO_4 + 2 KHSO_4

+ + ⟶ + + +

sulfuric acid + manganese dioxide + potassium iodide ⟶ water + iodine + manganese(II) sulfate + potassium bisulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + MnO_2 + KI ⟶ H_2O + I_2 + MnSO_4 + KHSO_4 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 H_2SO_4 + MnO_2 + 2 KI ⟶ 2 H_2O + I_2 + MnSO_4 + 2 KHSO_4 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 H_2SO_4 | 3 | -3 MnO_2 | 1 | -1 KI | 2 | -2 H_2O | 2 | 2 I_2 | 1 | 1 MnSO_4 | 1 | 1 KHSO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) MnO_2 | 1 | -1 | ([MnO2])^(-1) KI | 2 | -2 | ([KI])^(-2) H_2O | 2 | 2 | ([H2O])^2 I_2 | 1 | 1 | [I2] MnSO_4 | 1 | 1 | [MnSO4] KHSO_4 | 2 | 2 | ([KHSO4])^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 = ([H2SO4])^(-3) ([MnO2])^(-1) ([KI])^(-2) ([H2O])^2 [I2] [MnSO4] ([KHSO4])^2 = (([H2O])^2 [I2] [MnSO4] ([KHSO4])^2)/(([H2SO4])^3 [MnO2] ([KI])^2)

Construct the rate of reaction expression for: H_2SO_4 + MnO_2 + KI ⟶ H_2O + I_2 + MnSO_4 + KHSO_4 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 H_2SO_4 + MnO_2 + 2 KI ⟶ 2 H_2O + I_2 + MnSO_4 + 2 KHSO_4 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 H_2SO_4 | 3 | -3 MnO_2 | 1 | -1 KI | 2 | -2 H_2O | 2 | 2 I_2 | 1 | 1 MnSO_4 | 1 | 1 KHSO_4 | 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) KI | 2 | -2 | -1/2 (Δ[KI])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) I_2 | 1 | 1 | (Δ[I2])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(Δt) KHSO_4 | 2 | 2 | 1/2 (Δ[KHSO4])/(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[H2SO4])/(Δt) = -(Δ[MnO2])/(Δt) = -1/2 (Δ[KI])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[I2])/(Δt) = (Δ[MnSO4])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | manganese dioxide | potassium iodide | water | iodine | manganese(II) sulfate | potassium bisulfate formula | H_2SO_4 | MnO_2 | KI | H_2O | I_2 | MnSO_4 | KHSO_4 Hill formula | H_2O_4S | MnO_2 | IK | H_2O | I_2 | MnSO_4 | HKO_4S name | sulfuric acid | manganese dioxide | potassium iodide | water | iodine | manganese(II) sulfate | potassium bisulfate IUPAC name | sulfuric acid | dioxomanganese | potassium iodide | water | molecular iodine | manganese(+2) cation sulfate | potassium hydrogen sulfate

| sulfuric acid | manganese dioxide | potassium iodide | water | iodine | manganese(II) sulfate | potassium bisulfate molar mass | 98.07 g/mol | 86.936 g/mol | 166.0028 g/mol | 18.015 g/mol | 253.80894 g/mol | 150.99 g/mol | 136.16 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 10.371 °C | 535 °C | 681 °C | 0 °C | 113 °C | 710 °C | 214 °C boiling point | 279.6 °C | | 1330 °C | 99.9839 °C | 184 °C | | density | 1.8305 g/cm^3 | 5.03 g/cm^3 | 3.123 g/cm^3 | 1 g/cm^3 | 4.94 g/cm^3 | 3.25 g/cm^3 | 2.32 g/cm^3 solubility in water | very soluble | insoluble | | | | soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 0.0010227 Pa s (at 732.9 °C) | 8.9×10^-4 Pa s (at 25 °C) | 0.00227 Pa s (at 116 °C) | | odor | odorless | | | odorless | | |