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H2O + KMnO4 + C3H6 = KOH + MnO2 + C2H4(OH)2

Input interpretation

H_2O water + KMnO_4 potassium permanganate + C_3H_6 cyclopropane ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + HOCH_2CH_2OH ethylene glycol
H_2O water + KMnO_4 potassium permanganate + C_3H_6 cyclopropane ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + HOCH_2CH_2OH ethylene glycol

Balanced equation

Balance the chemical equation algebraically: H_2O + KMnO_4 + C_3H_6 ⟶ KOH + MnO_2 + HOCH_2CH_2OH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 C_3H_6 ⟶ c_4 KOH + c_5 MnO_2 + c_6 HOCH_2CH_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 + 6 c_3 = c_4 + 6 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: | 3 c_3 = 2 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 = 1 c_4 = 1 c_5 = 1 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 2 KMnO_4 + 2 C_3H_6 ⟶ 2 KOH + 2 MnO_2 + 3 HOCH_2CH_2OH
Balance the chemical equation algebraically: H_2O + KMnO_4 + C_3H_6 ⟶ KOH + MnO_2 + HOCH_2CH_2OH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 C_3H_6 ⟶ c_4 KOH + c_5 MnO_2 + c_6 HOCH_2CH_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 + 6 c_3 = c_4 + 6 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: | 3 c_3 = 2 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 = 1 c_4 = 1 c_5 = 1 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 2 KMnO_4 + 2 C_3H_6 ⟶ 2 KOH + 2 MnO_2 + 3 HOCH_2CH_2OH

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + potassium permanganate + cyclopropane ⟶ potassium hydroxide + manganese dioxide + ethylene glycol
water + potassium permanganate + cyclopropane ⟶ potassium hydroxide + manganese dioxide + ethylene glycol

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + C_3H_6 ⟶ KOH + MnO_2 + HOCH_2CH_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: 4 H_2O + 2 KMnO_4 + 2 C_3H_6 ⟶ 2 KOH + 2 MnO_2 + 3 HOCH_2CH_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 | 4 | -4 KMnO_4 | 2 | -2 C_3H_6 | 2 | -2 KOH | 2 | 2 MnO_2 | 2 | 2 HOCH_2CH_2OH | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) C_3H_6 | 2 | -2 | ([C3H6])^(-2) KOH | 2 | 2 | ([KOH])^2 MnO_2 | 2 | 2 | ([MnO2])^2 HOCH_2CH_2OH | 3 | 3 | ([HOCH2CH2OH])^3 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])^(-4) ([KMnO4])^(-2) ([C3H6])^(-2) ([KOH])^2 ([MnO2])^2 ([HOCH2CH2OH])^3 = (([KOH])^2 ([MnO2])^2 ([HOCH2CH2OH])^3)/(([H2O])^4 ([KMnO4])^2 ([C3H6])^2)
Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + C_3H_6 ⟶ KOH + MnO_2 + HOCH_2CH_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: 4 H_2O + 2 KMnO_4 + 2 C_3H_6 ⟶ 2 KOH + 2 MnO_2 + 3 HOCH_2CH_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 | 4 | -4 KMnO_4 | 2 | -2 C_3H_6 | 2 | -2 KOH | 2 | 2 MnO_2 | 2 | 2 HOCH_2CH_2OH | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) C_3H_6 | 2 | -2 | ([C3H6])^(-2) KOH | 2 | 2 | ([KOH])^2 MnO_2 | 2 | 2 | ([MnO2])^2 HOCH_2CH_2OH | 3 | 3 | ([HOCH2CH2OH])^3 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])^(-4) ([KMnO4])^(-2) ([C3H6])^(-2) ([KOH])^2 ([MnO2])^2 ([HOCH2CH2OH])^3 = (([KOH])^2 ([MnO2])^2 ([HOCH2CH2OH])^3)/(([H2O])^4 ([KMnO4])^2 ([C3H6])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O + KMnO_4 + C_3H_6 ⟶ KOH + MnO_2 + HOCH_2CH_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: 4 H_2O + 2 KMnO_4 + 2 C_3H_6 ⟶ 2 KOH + 2 MnO_2 + 3 HOCH_2CH_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 | 4 | -4 KMnO_4 | 2 | -2 C_3H_6 | 2 | -2 KOH | 2 | 2 MnO_2 | 2 | 2 HOCH_2CH_2OH | 3 | 3 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 | 4 | -4 | -1/4 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) C_3H_6 | 2 | -2 | -1/2 (Δ[C3H6])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) HOCH_2CH_2OH | 3 | 3 | 1/3 (Δ[HOCH2CH2OH])/(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[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/2 (Δ[C3H6])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = 1/3 (Δ[HOCH2CH2OH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + KMnO_4 + C_3H_6 ⟶ KOH + MnO_2 + HOCH_2CH_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: 4 H_2O + 2 KMnO_4 + 2 C_3H_6 ⟶ 2 KOH + 2 MnO_2 + 3 HOCH_2CH_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 | 4 | -4 KMnO_4 | 2 | -2 C_3H_6 | 2 | -2 KOH | 2 | 2 MnO_2 | 2 | 2 HOCH_2CH_2OH | 3 | 3 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 | 4 | -4 | -1/4 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) C_3H_6 | 2 | -2 | -1/2 (Δ[C3H6])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) HOCH_2CH_2OH | 3 | 3 | 1/3 (Δ[HOCH2CH2OH])/(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[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/2 (Δ[C3H6])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = 1/3 (Δ[HOCH2CH2OH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | potassium permanganate | cyclopropane | potassium hydroxide | manganese dioxide | ethylene glycol formula | H_2O | KMnO_4 | C_3H_6 | KOH | MnO_2 | HOCH_2CH_2OH Hill formula | H_2O | KMnO_4 | C_3H_6 | HKO | MnO_2 | C_2H_6O_2 name | water | potassium permanganate | cyclopropane | potassium hydroxide | manganese dioxide | ethylene glycol IUPAC name | water | potassium permanganate | cyclopropane | potassium hydroxide | dioxomanganese | ethylene glycol
| water | potassium permanganate | cyclopropane | potassium hydroxide | manganese dioxide | ethylene glycol formula | H_2O | KMnO_4 | C_3H_6 | KOH | MnO_2 | HOCH_2CH_2OH Hill formula | H_2O | KMnO_4 | C_3H_6 | HKO | MnO_2 | C_2H_6O_2 name | water | potassium permanganate | cyclopropane | potassium hydroxide | manganese dioxide | ethylene glycol IUPAC name | water | potassium permanganate | cyclopropane | potassium hydroxide | dioxomanganese | ethylene glycol

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