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H2O + KMnO4 + FeSO4 = KOH + MnO2 + FeOHSO4

Input interpretation

H_2O water + KMnO_4 potassium permanganate + FeSO_4 duretter ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + FeOHSO4
H_2O water + KMnO_4 potassium permanganate + FeSO_4 duretter ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + FeOHSO4

Balanced equation

Balance the chemical equation algebraically: H_2O + KMnO_4 + FeSO_4 ⟶ KOH + MnO_2 + FeOHSO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 FeSO_4 ⟶ c_4 KOH + c_5 MnO_2 + c_6 FeOHSO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn, Fe and S: H: | 2 c_1 = c_4 + c_6 O: | c_1 + 4 c_2 + 4 c_3 = c_4 + 2 c_5 + 5 c_6 K: | c_2 = c_4 Mn: | c_2 = c_5 Fe: | c_3 = c_6 S: | c_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 = 3 c_4 = 1 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + KMnO_4 + 3 FeSO_4 ⟶ KOH + MnO_2 + 3 FeOHSO4
Balance the chemical equation algebraically: H_2O + KMnO_4 + FeSO_4 ⟶ KOH + MnO_2 + FeOHSO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 FeSO_4 ⟶ c_4 KOH + c_5 MnO_2 + c_6 FeOHSO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn, Fe and S: H: | 2 c_1 = c_4 + c_6 O: | c_1 + 4 c_2 + 4 c_3 = c_4 + 2 c_5 + 5 c_6 K: | c_2 = c_4 Mn: | c_2 = c_5 Fe: | c_3 = c_6 S: | c_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 = 3 c_4 = 1 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + KMnO_4 + 3 FeSO_4 ⟶ KOH + MnO_2 + 3 FeOHSO4

Structures

+ + ⟶ + + FeOHSO4
+ + ⟶ + + FeOHSO4

Names

water + potassium permanganate + duretter ⟶ potassium hydroxide + manganese dioxide + FeOHSO4
water + potassium permanganate + duretter ⟶ potassium hydroxide + manganese dioxide + FeOHSO4

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + FeSO_4 ⟶ KOH + MnO_2 + FeOHSO4 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 + 3 FeSO_4 ⟶ KOH + MnO_2 + 3 FeOHSO4 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 FeSO_4 | 3 | -3 KOH | 1 | 1 MnO_2 | 1 | 1 FeOHSO4 | 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 | 2 | -2 | ([H2O])^(-2) KMnO_4 | 1 | -1 | ([KMnO4])^(-1) FeSO_4 | 3 | -3 | ([FeSO4])^(-3) KOH | 1 | 1 | [KOH] MnO_2 | 1 | 1 | [MnO2] FeOHSO4 | 3 | 3 | ([FeOHSO4])^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) ([FeSO4])^(-3) [KOH] [MnO2] ([FeOHSO4])^3 = ([KOH] [MnO2] ([FeOHSO4])^3)/(([H2O])^2 [KMnO4] ([FeSO4])^3)
Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + FeSO_4 ⟶ KOH + MnO_2 + FeOHSO4 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 + 3 FeSO_4 ⟶ KOH + MnO_2 + 3 FeOHSO4 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 FeSO_4 | 3 | -3 KOH | 1 | 1 MnO_2 | 1 | 1 FeOHSO4 | 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 | 2 | -2 | ([H2O])^(-2) KMnO_4 | 1 | -1 | ([KMnO4])^(-1) FeSO_4 | 3 | -3 | ([FeSO4])^(-3) KOH | 1 | 1 | [KOH] MnO_2 | 1 | 1 | [MnO2] FeOHSO4 | 3 | 3 | ([FeOHSO4])^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) ([FeSO4])^(-3) [KOH] [MnO2] ([FeOHSO4])^3 = ([KOH] [MnO2] ([FeOHSO4])^3)/(([H2O])^2 [KMnO4] ([FeSO4])^3)

Rate of reaction

Construct the rate of reaction expression for: H_2O + KMnO_4 + FeSO_4 ⟶ KOH + MnO_2 + FeOHSO4 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 + 3 FeSO_4 ⟶ KOH + MnO_2 + 3 FeOHSO4 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 FeSO_4 | 3 | -3 KOH | 1 | 1 MnO_2 | 1 | 1 FeOHSO4 | 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KMnO_4 | 1 | -1 | -(Δ[KMnO4])/(Δt) FeSO_4 | 3 | -3 | -1/3 (Δ[FeSO4])/(Δt) KOH | 1 | 1 | (Δ[KOH])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(Δt) FeOHSO4 | 3 | 3 | 1/3 (Δ[FeOHSO4])/(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) = -1/3 (Δ[FeSO4])/(Δt) = (Δ[KOH])/(Δt) = (Δ[MnO2])/(Δt) = 1/3 (Δ[FeOHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + KMnO_4 + FeSO_4 ⟶ KOH + MnO_2 + FeOHSO4 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 + 3 FeSO_4 ⟶ KOH + MnO_2 + 3 FeOHSO4 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 FeSO_4 | 3 | -3 KOH | 1 | 1 MnO_2 | 1 | 1 FeOHSO4 | 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KMnO_4 | 1 | -1 | -(Δ[KMnO4])/(Δt) FeSO_4 | 3 | -3 | -1/3 (Δ[FeSO4])/(Δt) KOH | 1 | 1 | (Δ[KOH])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(Δt) FeOHSO4 | 3 | 3 | 1/3 (Δ[FeOHSO4])/(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) = -1/3 (Δ[FeSO4])/(Δt) = (Δ[KOH])/(Δt) = (Δ[MnO2])/(Δt) = 1/3 (Δ[FeOHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | potassium permanganate | duretter | potassium hydroxide | manganese dioxide | FeOHSO4 formula | H_2O | KMnO_4 | FeSO_4 | KOH | MnO_2 | FeOHSO4 Hill formula | H_2O | KMnO_4 | FeO_4S | HKO | MnO_2 | HFeO5S name | water | potassium permanganate | duretter | potassium hydroxide | manganese dioxide | IUPAC name | water | potassium permanganate | iron(+2) cation sulfate | potassium hydroxide | dioxomanganese |
| water | potassium permanganate | duretter | potassium hydroxide | manganese dioxide | FeOHSO4 formula | H_2O | KMnO_4 | FeSO_4 | KOH | MnO_2 | FeOHSO4 Hill formula | H_2O | KMnO_4 | FeO_4S | HKO | MnO_2 | HFeO5S name | water | potassium permanganate | duretter | potassium hydroxide | manganese dioxide | IUPAC name | water | potassium permanganate | iron(+2) cation sulfate | potassium hydroxide | dioxomanganese |

Substance properties

| water | potassium permanganate | duretter | potassium hydroxide | manganese dioxide | FeOHSO4 molar mass | 18.015 g/mol | 158.03 g/mol | 151.9 g/mol | 56.105 g/mol | 86.936 g/mol | 168.91 g/mol phase | liquid (at STP) | solid (at STP) | | solid (at STP) | solid (at STP) | melting point | 0 °C | 240 °C | | 406 °C | 535 °C | boiling point | 99.9839 °C | | | 1327 °C | | density | 1 g/cm^3 | 1 g/cm^3 | 2.841 g/cm^3 | 2.044 g/cm^3 | 5.03 g/cm^3 | solubility in water | | | | soluble | insoluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.001 Pa s (at 550 °C) | | odor | odorless | odorless | | | |
| water | potassium permanganate | duretter | potassium hydroxide | manganese dioxide | FeOHSO4 molar mass | 18.015 g/mol | 158.03 g/mol | 151.9 g/mol | 56.105 g/mol | 86.936 g/mol | 168.91 g/mol phase | liquid (at STP) | solid (at STP) | | solid (at STP) | solid (at STP) | melting point | 0 °C | 240 °C | | 406 °C | 535 °C | boiling point | 99.9839 °C | | | 1327 °C | | density | 1 g/cm^3 | 1 g/cm^3 | 2.841 g/cm^3 | 2.044 g/cm^3 | 5.03 g/cm^3 | solubility in water | | | | soluble | insoluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.001 Pa s (at 550 °C) | | odor | odorless | odorless | | | |

Units

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