KMnO4 + C2H4 = H2O + MnO2 + K2CO3

KMnO_4 potassium permanganate + CH_2=CH_2 ethylene ⟶ H_2O water + MnO_2 manganese dioxide + K_2CO_3 pearl ash

Balance the chemical equation algebraically: KMnO_4 + CH_2=CH_2 ⟶ H_2O + MnO_2 + K_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 CH_2=CH_2 ⟶ c_3 H_2O + c_4 MnO_2 + c_5 K_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, C and H: K: | c_1 = 2 c_5 Mn: | c_1 = c_4 O: | 4 c_1 = c_3 + 2 c_4 + 3 c_5 C: | 2 c_2 = c_5 H: | 4 c_2 = 2 c_3 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 = 4 c_2 = 1 c_3 = 2 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 + CH_2=CH_2 ⟶ 2 H_2O + 4 MnO_2 + 2 K_2CO_3

+ ⟶ + +

potassium permanganate + ethylene ⟶ water + manganese dioxide + pearl ash

| potassium permanganate | ethylene | water | manganese dioxide | pearl ash molecular free energy | -737.6 kJ/mol | 68 kJ/mol | -237.1 kJ/mol | -465.1 kJ/mol | -1064 kJ/mol total free energy | -2950 kJ/mol | 68 kJ/mol | -474.2 kJ/mol | -1860 kJ/mol | -2127 kJ/mol | G_initial = -2882 kJ/mol | | G_final = -4462 kJ/mol | | ΔG_rxn^0 | -4462 kJ/mol - -2882 kJ/mol = -1579 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: KMnO_4 + CH_2=CH_2 ⟶ H_2O + MnO_2 + K_2CO_3 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: 4 KMnO_4 + CH_2=CH_2 ⟶ 2 H_2O + 4 MnO_2 + 2 K_2CO_3 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 KMnO_4 | 4 | -4 CH_2=CH_2 | 1 | -1 H_2O | 2 | 2 MnO_2 | 4 | 4 K_2CO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 4 | -4 | ([KMnO4])^(-4) CH_2=CH_2 | 1 | -1 | ([CH2=CH2])^(-1) H_2O | 2 | 2 | ([H2O])^2 MnO_2 | 4 | 4 | ([MnO2])^4 K_2CO_3 | 2 | 2 | ([K2CO3])^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 = ([KMnO4])^(-4) ([CH2=CH2])^(-1) ([H2O])^2 ([MnO2])^4 ([K2CO3])^2 = (([H2O])^2 ([MnO2])^4 ([K2CO3])^2)/(([KMnO4])^4 [CH2=CH2])

Construct the rate of reaction expression for: KMnO_4 + CH_2=CH_2 ⟶ H_2O + MnO_2 + K_2CO_3 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: 4 KMnO_4 + CH_2=CH_2 ⟶ 2 H_2O + 4 MnO_2 + 2 K_2CO_3 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 KMnO_4 | 4 | -4 CH_2=CH_2 | 1 | -1 H_2O | 2 | 2 MnO_2 | 4 | 4 K_2CO_3 | 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 KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) CH_2=CH_2 | 1 | -1 | -(Δ[CH2=CH2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(Δt) K_2CO_3 | 2 | 2 | 1/2 (Δ[K2CO3])/(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 = -1/4 (Δ[KMnO4])/(Δt) = -(Δ[CH2=CH2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/4 (Δ[MnO2])/(Δt) = 1/2 (Δ[K2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | ethylene | water | manganese dioxide | pearl ash formula | KMnO_4 | CH_2=CH_2 | H_2O | MnO_2 | K_2CO_3 Hill formula | KMnO_4 | C_2H_4 | H_2O | MnO_2 | CK_2O_3 name | potassium permanganate | ethylene | water | manganese dioxide | pearl ash IUPAC name | potassium permanganate | ethylene | water | dioxomanganese | dipotassium carbonate

| potassium permanganate | ethylene | water | manganese dioxide | pearl ash molar mass | 158.03 g/mol | 28.054 g/mol | 18.015 g/mol | 86.936 g/mol | 138.2 g/mol phase | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 240 °C | -169 °C | 0 °C | 535 °C | 891 °C boiling point | | -104 °C | 99.9839 °C | | density | 1 g/cm^3 | 1.153 g/cm^3 (at 25 °C) | 1 g/cm^3 | 5.03 g/cm^3 | 2.43 g/cm^3 solubility in water | | insoluble | | insoluble | soluble surface tension | | 0.0181 N/m | 0.0728 N/m | | dynamic viscosity | | 1.034×10^-5 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | | odorless | |