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H2O + KMnO4 + C6H12 = KOH + MnO2 + C6H12(OH)3

Input interpretation

H_2O water + KMnO_4 potassium permanganate + C_6H_12 cyclohexane ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + C6H12(OH)3
H_2O water + KMnO_4 potassium permanganate + C_6H_12 cyclohexane ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + C6H12(OH)3

Balanced equation

Balance the chemical equation algebraically: H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 C_6H_12 ⟶ c_4 KOH + c_5 MnO_2 + c_6 C6H12(OH)3 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 + 12 c_3 = c_4 + 15 c_6 O: | c_1 + 4 c_2 = c_4 + 2 c_5 + 3 c_6 K: | c_2 = c_4 Mn: | c_2 = c_5 C: | 6 c_3 = 6 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)3
Balance the chemical equation algebraically: H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 C_6H_12 ⟶ c_4 KOH + c_5 MnO_2 + c_6 C6H12(OH)3 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 + 12 c_3 = c_4 + 15 c_6 O: | c_1 + 4 c_2 = c_4 + 2 c_5 + 3 c_6 K: | c_2 = c_4 Mn: | c_2 = c_5 C: | 6 c_3 = 6 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)3

Structures

+ + ⟶ + + C6H12(OH)3
+ + ⟶ + + C6H12(OH)3

Names

water + potassium permanganate + cyclohexane ⟶ potassium hydroxide + manganese dioxide + C6H12(OH)3
water + potassium permanganate + cyclohexane ⟶ potassium hydroxide + manganese dioxide + C6H12(OH)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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: 2 H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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 H_2O | 2 | -2 KMnO_4 | 1 | -1 C_6H_12 | 1 | -1 KOH | 1 | 1 MnO_2 | 1 | 1 C6H12(OH)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) KMnO_4 | 1 | -1 | ([KMnO4])^(-1) C_6H_12 | 1 | -1 | ([C6H12])^(-1) KOH | 1 | 1 | [KOH] MnO_2 | 1 | 1 | [MnO2] C6H12(OH)3 | 1 | 1 | [C6H12(OH)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])^(-2) ([KMnO4])^(-1) ([C6H12])^(-1) [KOH] [MnO2] [C6H12(OH)3] = ([KOH] [MnO2] [C6H12(OH)3])/(([H2O])^2 [KMnO4] [C6H12])
Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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: 2 H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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 H_2O | 2 | -2 KMnO_4 | 1 | -1 C_6H_12 | 1 | -1 KOH | 1 | 1 MnO_2 | 1 | 1 C6H12(OH)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) KMnO_4 | 1 | -1 | ([KMnO4])^(-1) C_6H_12 | 1 | -1 | ([C6H12])^(-1) KOH | 1 | 1 | [KOH] MnO_2 | 1 | 1 | [MnO2] C6H12(OH)3 | 1 | 1 | [C6H12(OH)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])^(-2) ([KMnO4])^(-1) ([C6H12])^(-1) [KOH] [MnO2] [C6H12(OH)3] = ([KOH] [MnO2] [C6H12(OH)3])/(([H2O])^2 [KMnO4] [C6H12])

Rate of reaction

Construct the rate of reaction expression for: H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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: 2 H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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 H_2O | 2 | -2 KMnO_4 | 1 | -1 C_6H_12 | 1 | -1 KOH | 1 | 1 MnO_2 | 1 | 1 C6H12(OH)3 | 1 | 1 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KMnO_4 | 1 | -1 | -(Δ[KMnO4])/(Δt) C_6H_12 | 1 | -1 | -(Δ[C6H12])/(Δt) KOH | 1 | 1 | (Δ[KOH])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(Δt) C6H12(OH)3 | 1 | 1 | (Δ[C6H12(OH)3])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[KMnO4])/(Δt) = -(Δ[C6H12])/(Δt) = (Δ[KOH])/(Δt) = (Δ[MnO2])/(Δt) = (Δ[C6H12(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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: 2 H_2O + KMnO_4 + C_6H_12 ⟶ KOH + MnO_2 + C6H12(OH)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 H_2O | 2 | -2 KMnO_4 | 1 | -1 C_6H_12 | 1 | -1 KOH | 1 | 1 MnO_2 | 1 | 1 C6H12(OH)3 | 1 | 1 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KMnO_4 | 1 | -1 | -(Δ[KMnO4])/(Δt) C_6H_12 | 1 | -1 | -(Δ[C6H12])/(Δt) KOH | 1 | 1 | (Δ[KOH])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(Δt) C6H12(OH)3 | 1 | 1 | (Δ[C6H12(OH)3])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[KMnO4])/(Δt) = -(Δ[C6H12])/(Δt) = (Δ[KOH])/(Δt) = (Δ[MnO2])/(Δt) = (Δ[C6H12(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | potassium permanganate | cyclohexane | potassium hydroxide | manganese dioxide | C6H12(OH)3 formula | H_2O | KMnO_4 | C_6H_12 | KOH | MnO_2 | C6H12(OH)3 Hill formula | H_2O | KMnO_4 | C_6H_12 | HKO | MnO_2 | C6H15O3 name | water | potassium permanganate | cyclohexane | potassium hydroxide | manganese dioxide | IUPAC name | water | potassium permanganate | cyclohexane | potassium hydroxide | dioxomanganese |
| water | potassium permanganate | cyclohexane | potassium hydroxide | manganese dioxide | C6H12(OH)3 formula | H_2O | KMnO_4 | C_6H_12 | KOH | MnO_2 | C6H12(OH)3 Hill formula | H_2O | KMnO_4 | C_6H_12 | HKO | MnO_2 | C6H15O3 name | water | potassium permanganate | cyclohexane | potassium hydroxide | manganese dioxide | IUPAC name | water | potassium permanganate | cyclohexane | potassium hydroxide | dioxomanganese |

Substance properties

| water | potassium permanganate | cyclohexane | potassium hydroxide | manganese dioxide | C6H12(OH)3 molar mass | 18.015 g/mol | 158.03 g/mol | 84.16 g/mol | 56.105 g/mol | 86.936 g/mol | 135.18 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | 240 °C | 5.5 °C | 406 °C | 535 °C | boiling point | 99.9839 °C | | 80.7 °C | 1327 °C | | density | 1 g/cm^3 | 1 g/cm^3 | 0.779 g/cm^3 | 2.044 g/cm^3 | 5.03 g/cm^3 | solubility in water | | | insoluble | soluble | insoluble | surface tension | 0.0728 N/m | | 0.02499 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.94×10^-4 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | | odor | odorless | odorless | | | |
| water | potassium permanganate | cyclohexane | potassium hydroxide | manganese dioxide | C6H12(OH)3 molar mass | 18.015 g/mol | 158.03 g/mol | 84.16 g/mol | 56.105 g/mol | 86.936 g/mol | 135.18 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | 240 °C | 5.5 °C | 406 °C | 535 °C | boiling point | 99.9839 °C | | 80.7 °C | 1327 °C | | density | 1 g/cm^3 | 1 g/cm^3 | 0.779 g/cm^3 | 2.044 g/cm^3 | 5.03 g/cm^3 | solubility in water | | | insoluble | soluble | insoluble | surface tension | 0.0728 N/m | | 0.02499 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.94×10^-4 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | | odor | odorless | odorless | | | |

Units

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