H2O + KMnO4 + C4H8 = KOH + MnO2 + C3H6(OH)2

H_2O water + KMnO_4 potassium permanganate + (CH_3)_2C=CH_2 isobutylene ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + CH_3CH(OH)CH_2OH propylene glycol

Balance the chemical equation algebraically: H_2O + KMnO_4 + (CH_3)_2C=CH_2 ⟶ KOH + MnO_2 + CH_3CH(OH)CH_2OH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 (CH_3)_2C=CH_2 ⟶ c_4 KOH + c_5 MnO_2 + c_6 CH_3CH(OH)CH_2OH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn and C: H: | 2 c_1 + 8 c_3 = c_4 + 8 c_6 O: | c_1 + 4 c_2 = c_4 + 2 c_5 + 2 c_6 K: | c_2 = c_4 Mn: | c_2 = c_5 C: | 4 c_3 = 3 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 = 2 c_2 = 1 c_3 = 9/8 c_4 = 1 c_5 = 1 c_6 = 3/2 Multiply by the least common denominator, 8, to eliminate fractional coefficients: c_1 = 16 c_2 = 8 c_3 = 9 c_4 = 8 c_5 = 8 c_6 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 H_2O + 8 KMnO_4 + 9 (CH_3)_2C=CH_2 ⟶ 8 KOH + 8 MnO_2 + 12 CH_3CH(OH)CH_2OH

+ + ⟶ + +

water + potassium permanganate + isobutylene ⟶ potassium hydroxide + manganese dioxide + propylene glycol

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + (CH_3)_2C=CH_2 ⟶ KOH + MnO_2 + CH_3CH(OH)CH_2OH 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: 16 H_2O + 8 KMnO_4 + 9 (CH_3)_2C=CH_2 ⟶ 8 KOH + 8 MnO_2 + 12 CH_3CH(OH)CH_2OH 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_2O | 16 | -16 KMnO_4 | 8 | -8 (CH_3)_2C=CH_2 | 9 | -9 KOH | 8 | 8 MnO_2 | 8 | 8 CH_3CH(OH)CH_2OH | 12 | 12 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 16 | -16 | ([H2O])^(-16) KMnO_4 | 8 | -8 | ([KMnO4])^(-8) (CH_3)_2C=CH_2 | 9 | -9 | ([(CH3)2C=CH2])^(-9) KOH | 8 | 8 | ([KOH])^8 MnO_2 | 8 | 8 | ([MnO2])^8 CH_3CH(OH)CH_2OH | 12 | 12 | ([CH3CH(OH)CH2OH])^12 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 = ([H2O])^(-16) ([KMnO4])^(-8) ([(CH3)2C=CH2])^(-9) ([KOH])^8 ([MnO2])^8 ([CH3CH(OH)CH2OH])^12 = (([KOH])^8 ([MnO2])^8 ([CH3CH(OH)CH2OH])^12)/(([H2O])^16 ([KMnO4])^8 ([(CH3)2C=CH2])^9)

Construct the rate of reaction expression for: H_2O + KMnO_4 + (CH_3)_2C=CH_2 ⟶ KOH + MnO_2 + CH_3CH(OH)CH_2OH 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: 16 H_2O + 8 KMnO_4 + 9 (CH_3)_2C=CH_2 ⟶ 8 KOH + 8 MnO_2 + 12 CH_3CH(OH)CH_2OH 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_2O | 16 | -16 KMnO_4 | 8 | -8 (CH_3)_2C=CH_2 | 9 | -9 KOH | 8 | 8 MnO_2 | 8 | 8 CH_3CH(OH)CH_2OH | 12 | 12 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_2O | 16 | -16 | -1/16 (Δ[H2O])/(Δt) KMnO_4 | 8 | -8 | -1/8 (Δ[KMnO4])/(Δt) (CH_3)_2C=CH_2 | 9 | -9 | -1/9 (Δ[(CH3)2C=CH2])/(Δt) KOH | 8 | 8 | 1/8 (Δ[KOH])/(Δt) MnO_2 | 8 | 8 | 1/8 (Δ[MnO2])/(Δt) CH_3CH(OH)CH_2OH | 12 | 12 | 1/12 (Δ[CH3CH(OH)CH2OH])/(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 = -1/16 (Δ[H2O])/(Δt) = -1/8 (Δ[KMnO4])/(Δt) = -1/9 (Δ[(CH3)2C=CH2])/(Δt) = 1/8 (Δ[KOH])/(Δt) = 1/8 (Δ[MnO2])/(Δt) = 1/12 (Δ[CH3CH(OH)CH2OH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium permanganate | isobutylene | potassium hydroxide | manganese dioxide | propylene glycol formula | H_2O | KMnO_4 | (CH_3)_2C=CH_2 | KOH | MnO_2 | CH_3CH(OH)CH_2OH Hill formula | H_2O | KMnO_4 | C_4H_8 | HKO | MnO_2 | C_3H_8O_2 name | water | potassium permanganate | isobutylene | potassium hydroxide | manganese dioxide | propylene glycol IUPAC name | water | potassium permanganate | 2-methylprop-1-ene | potassium hydroxide | dioxomanganese | propane-1, 2-diol

| water | potassium permanganate | isobutylene | potassium hydroxide | manganese dioxide | propylene glycol molar mass | 18.015 g/mol | 158.03 g/mol | 56.11 g/mol | 56.105 g/mol | 86.936 g/mol | 76.09 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) melting point | 0 °C | 240 °C | -140 °C | 406 °C | 535 °C | -60 °C boiling point | 99.9839 °C | | -6.9 °C | 1327 °C | | 187 °C density | 1 g/cm^3 | 1 g/cm^3 | 0.5942 g/cm^3 (at 20 °C) | 2.044 g/cm^3 | 5.03 g/cm^3 | 1.036 g/cm^3 solubility in water | | | insoluble | soluble | insoluble | miscible surface tension | 0.0728 N/m | | 0.0123 N/m | | | 0.0401 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.084×10^-6 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | | 0.0404 Pa s (at 25 °C) odor | odorless | odorless | | | | odorless