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O2 + MnO2 + K2MnO4 = KMnO4

Input interpretation

O_2 oxygen + MnO_2 manganese dioxide + K_2MnO_4 potassium manganate ⟶ KMnO_4 potassium permanganate
O_2 oxygen + MnO_2 manganese dioxide + K_2MnO_4 potassium manganate ⟶ KMnO_4 potassium permanganate

Balanced equation

Balance the chemical equation algebraically: O_2 + MnO_2 + K_2MnO_4 ⟶ KMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 MnO_2 + c_3 K_2MnO_4 ⟶ c_4 KMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Mn and K: O: | 2 c_1 + 2 c_2 + 4 c_3 = 4 c_4 Mn: | c_2 + c_3 = c_4 K: | 2 c_3 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + MnO_2 + K_2MnO_4 ⟶ 2 KMnO_4
Balance the chemical equation algebraically: O_2 + MnO_2 + K_2MnO_4 ⟶ KMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 MnO_2 + c_3 K_2MnO_4 ⟶ c_4 KMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Mn and K: O: | 2 c_1 + 2 c_2 + 4 c_3 = 4 c_4 Mn: | c_2 + c_3 = c_4 K: | 2 c_3 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + MnO_2 + K_2MnO_4 ⟶ 2 KMnO_4

Structures

+ + ⟶
+ + ⟶

Names

oxygen + manganese dioxide + potassium manganate ⟶ potassium permanganate
oxygen + manganese dioxide + potassium manganate ⟶ potassium permanganate

Equilibrium constant

Construct the equilibrium constant, K, expression for: O_2 + MnO_2 + K_2MnO_4 ⟶ KMnO_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: O_2 + MnO_2 + K_2MnO_4 ⟶ 2 KMnO_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 O_2 | 1 | -1 MnO_2 | 1 | -1 K_2MnO_4 | 1 | -1 KMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) MnO_2 | 1 | -1 | ([MnO2])^(-1) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) KMnO_4 | 2 | 2 | ([KMnO4])^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 = ([O2])^(-1) ([MnO2])^(-1) ([K2MnO4])^(-1) ([KMnO4])^2 = ([KMnO4])^2/([O2] [MnO2] [K2MnO4])
Construct the equilibrium constant, K, expression for: O_2 + MnO_2 + K_2MnO_4 ⟶ KMnO_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: O_2 + MnO_2 + K_2MnO_4 ⟶ 2 KMnO_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 O_2 | 1 | -1 MnO_2 | 1 | -1 K_2MnO_4 | 1 | -1 KMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) MnO_2 | 1 | -1 | ([MnO2])^(-1) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) KMnO_4 | 2 | 2 | ([KMnO4])^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 = ([O2])^(-1) ([MnO2])^(-1) ([K2MnO4])^(-1) ([KMnO4])^2 = ([KMnO4])^2/([O2] [MnO2] [K2MnO4])

Rate of reaction

Construct the rate of reaction expression for: O_2 + MnO_2 + K_2MnO_4 ⟶ KMnO_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: O_2 + MnO_2 + K_2MnO_4 ⟶ 2 KMnO_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 O_2 | 1 | -1 MnO_2 | 1 | -1 K_2MnO_4 | 1 | -1 KMnO_4 | 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 O_2 | 1 | -1 | -(Δ[O2])/(Δt) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) KMnO_4 | 2 | 2 | 1/2 (Δ[KMnO4])/(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 = -(Δ[O2])/(Δt) = -(Δ[MnO2])/(Δt) = -(Δ[K2MnO4])/(Δt) = 1/2 (Δ[KMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: O_2 + MnO_2 + K_2MnO_4 ⟶ KMnO_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: O_2 + MnO_2 + K_2MnO_4 ⟶ 2 KMnO_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 O_2 | 1 | -1 MnO_2 | 1 | -1 K_2MnO_4 | 1 | -1 KMnO_4 | 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 O_2 | 1 | -1 | -(Δ[O2])/(Δt) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) KMnO_4 | 2 | 2 | 1/2 (Δ[KMnO4])/(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 = -(Δ[O2])/(Δt) = -(Δ[MnO2])/(Δt) = -(Δ[K2MnO4])/(Δt) = 1/2 (Δ[KMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| oxygen | manganese dioxide | potassium manganate | potassium permanganate formula | O_2 | MnO_2 | K_2MnO_4 | KMnO_4 name | oxygen | manganese dioxide | potassium manganate | potassium permanganate IUPAC name | molecular oxygen | dioxomanganese | dipotassium dioxido-dioxomanganese | potassium permanganate
| oxygen | manganese dioxide | potassium manganate | potassium permanganate formula | O_2 | MnO_2 | K_2MnO_4 | KMnO_4 name | oxygen | manganese dioxide | potassium manganate | potassium permanganate IUPAC name | molecular oxygen | dioxomanganese | dipotassium dioxido-dioxomanganese | potassium permanganate

Substance properties

| oxygen | manganese dioxide | potassium manganate | potassium permanganate molar mass | 31.998 g/mol | 86.936 g/mol | 197.13 g/mol | 158.03 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -218 °C | 535 °C | 190 °C | 240 °C boiling point | -183 °C | | | density | 0.001429 g/cm^3 (at 0 °C) | 5.03 g/cm^3 | | 1 g/cm^3 solubility in water | | insoluble | decomposes | surface tension | 0.01347 N/m | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | odorless
| oxygen | manganese dioxide | potassium manganate | potassium permanganate molar mass | 31.998 g/mol | 86.936 g/mol | 197.13 g/mol | 158.03 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -218 °C | 535 °C | 190 °C | 240 °C boiling point | -183 °C | | | density | 0.001429 g/cm^3 (at 0 °C) | 5.03 g/cm^3 | | 1 g/cm^3 solubility in water | | insoluble | decomposes | surface tension | 0.01347 N/m | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | odorless

Units

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