H2SO4 + KMnO4 + MgI2 = H2O + K2SO4 + I2 + MnSO4 + MgSO4

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + MgI_2 magnesium iodide ⟶ H_2O water + K_2SO_4 potassium sulfate + I_2 iodine + MnSO_4 manganese(II) sulfate + MgSO_4 magnesium sulfate

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + MgI_2 ⟶ H_2O + K_2SO_4 + I_2 + MnSO_4 + MgSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 MgI_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 I_2 + c_7 MnSO_4 + c_8 MgSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn, I and Mg: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_7 + 4 c_8 S: | c_1 = c_5 + c_7 + c_8 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 I: | 2 c_3 = 2 c_6 Mg: | c_3 = c_8 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 5 c_4 = 8 c_5 = 1 c_6 = 5 c_7 = 2 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 2 KMnO_4 + 5 MgI_2 ⟶ 8 H_2O + K_2SO_4 + 5 I_2 + 2 MnSO_4 + 5 MgSO_4

+ + ⟶ + + + +

sulfuric acid + potassium permanganate + magnesium iodide ⟶ water + potassium sulfate + iodine + manganese(II) sulfate + magnesium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + MgI_2 ⟶ H_2O + K_2SO_4 + I_2 + MnSO_4 + MgSO_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: 8 H_2SO_4 + 2 KMnO_4 + 5 MgI_2 ⟶ 8 H_2O + K_2SO_4 + 5 I_2 + 2 MnSO_4 + 5 MgSO_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 | 8 | -8 KMnO_4 | 2 | -2 MgI_2 | 5 | -5 H_2O | 8 | 8 K_2SO_4 | 1 | 1 I_2 | 5 | 5 MnSO_4 | 2 | 2 MgSO_4 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 8 | -8 | ([H2SO4])^(-8) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) MgI_2 | 5 | -5 | ([MgI2])^(-5) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 1 | 1 | [K2SO4] I_2 | 5 | 5 | ([I2])^5 MnSO_4 | 2 | 2 | ([MnSO4])^2 MgSO_4 | 5 | 5 | ([MgSO4])^5 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])^(-8) ([KMnO4])^(-2) ([MgI2])^(-5) ([H2O])^8 [K2SO4] ([I2])^5 ([MnSO4])^2 ([MgSO4])^5 = (([H2O])^8 [K2SO4] ([I2])^5 ([MnSO4])^2 ([MgSO4])^5)/(([H2SO4])^8 ([KMnO4])^2 ([MgI2])^5)

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + MgI_2 ⟶ H_2O + K_2SO_4 + I_2 + MnSO_4 + MgSO_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: 8 H_2SO_4 + 2 KMnO_4 + 5 MgI_2 ⟶ 8 H_2O + K_2SO_4 + 5 I_2 + 2 MnSO_4 + 5 MgSO_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 | 8 | -8 KMnO_4 | 2 | -2 MgI_2 | 5 | -5 H_2O | 8 | 8 K_2SO_4 | 1 | 1 I_2 | 5 | 5 MnSO_4 | 2 | 2 MgSO_4 | 5 | 5 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 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) MgI_2 | 5 | -5 | -1/5 (Δ[MgI2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) I_2 | 5 | 5 | 1/5 (Δ[I2])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) MgSO_4 | 5 | 5 | 1/5 (Δ[MgSO4])/(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 = -1/8 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[MgI2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/5 (Δ[I2])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/5 (Δ[MgSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium permanganate | magnesium iodide | water | potassium sulfate | iodine | manganese(II) sulfate | magnesium sulfate formula | H_2SO_4 | KMnO_4 | MgI_2 | H_2O | K_2SO_4 | I_2 | MnSO_4 | MgSO_4 Hill formula | H_2O_4S | KMnO_4 | I_2Mg | H_2O | K_2O_4S | I_2 | MnSO_4 | MgO_4S name | sulfuric acid | potassium permanganate | magnesium iodide | water | potassium sulfate | iodine | manganese(II) sulfate | magnesium sulfate IUPAC name | sulfuric acid | potassium permanganate | magnesium diiodide | water | dipotassium sulfate | molecular iodine | manganese(+2) cation sulfate | magnesium sulfate

| sulfuric acid | potassium permanganate | magnesium iodide | water | potassium sulfate | iodine | manganese(II) sulfate | magnesium sulfate molar mass | 98.07 g/mol | 158.03 g/mol | 278.114 g/mol | 18.015 g/mol | 174.25 g/mol | 253.80894 g/mol | 150.99 g/mol | 120.4 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 | 240 °C | 637 °C | 0 °C | | 113 °C | 710 °C | boiling point | 279.6 °C | | | 99.9839 °C | | 184 °C | | density | 1.8305 g/cm^3 | 1 g/cm^3 | 4.43 g/cm^3 | 1 g/cm^3 | | 4.94 g/cm^3 | 3.25 g/cm^3 | solubility in water | very soluble | | | | soluble | | soluble | soluble surface tension | 0.0735 N/m | | | 0.0728 N/m | | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | 0.00227 Pa s (at 116 °C) | | odor | odorless | odorless | odorless | odorless | | | |