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H2SO4 + KMnO4 + FeO = H2O + K2SO4 + Fe2O3 + MnO

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + FeO iron(II) oxide ⟶ H_2O water + K_2SO_4 potassium sulfate + Fe_2O_3 iron(III) oxide + MnO manganese monoxide
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + FeO iron(II) oxide ⟶ H_2O water + K_2SO_4 potassium sulfate + Fe_2O_3 iron(III) oxide + MnO manganese monoxide

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + FeO ⟶ H_2O + K_2SO_4 + Fe_2O_3 + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 FeO ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Fe_2O_3 + c_7 MnO Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 3 c_6 + c_7 S: | c_1 = c_5 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 Fe: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 10 c_4 = 1 c_5 = 1 c_6 = 5 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 2 KMnO_4 + 10 FeO ⟶ H_2O + K_2SO_4 + 5 Fe_2O_3 + 2 MnO
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + FeO ⟶ H_2O + K_2SO_4 + Fe_2O_3 + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 FeO ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Fe_2O_3 + c_7 MnO Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 3 c_6 + c_7 S: | c_1 = c_5 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 Fe: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 10 c_4 = 1 c_5 = 1 c_6 = 5 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 2 KMnO_4 + 10 FeO ⟶ H_2O + K_2SO_4 + 5 Fe_2O_3 + 2 MnO

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + potassium permanganate + iron(II) oxide ⟶ water + potassium sulfate + iron(III) oxide + manganese monoxide
sulfuric acid + potassium permanganate + iron(II) oxide ⟶ water + potassium sulfate + iron(III) oxide + manganese monoxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + FeO ⟶ H_2O + K_2SO_4 + Fe_2O_3 + MnO 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: H_2SO_4 + 2 KMnO_4 + 10 FeO ⟶ H_2O + K_2SO_4 + 5 Fe_2O_3 + 2 MnO 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_2SO_4 | 1 | -1 KMnO_4 | 2 | -2 FeO | 10 | -10 H_2O | 1 | 1 K_2SO_4 | 1 | 1 Fe_2O_3 | 5 | 5 MnO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) FeO | 10 | -10 | ([FeO])^(-10) H_2O | 1 | 1 | [H2O] K_2SO_4 | 1 | 1 | [K2SO4] Fe_2O_3 | 5 | 5 | ([Fe2O3])^5 MnO | 2 | 2 | ([MnO])^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 = ([H2SO4])^(-1) ([KMnO4])^(-2) ([FeO])^(-10) [H2O] [K2SO4] ([Fe2O3])^5 ([MnO])^2 = ([H2O] [K2SO4] ([Fe2O3])^5 ([MnO])^2)/([H2SO4] ([KMnO4])^2 ([FeO])^10)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + FeO ⟶ H_2O + K_2SO_4 + Fe_2O_3 + MnO 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: H_2SO_4 + 2 KMnO_4 + 10 FeO ⟶ H_2O + K_2SO_4 + 5 Fe_2O_3 + 2 MnO 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_2SO_4 | 1 | -1 KMnO_4 | 2 | -2 FeO | 10 | -10 H_2O | 1 | 1 K_2SO_4 | 1 | 1 Fe_2O_3 | 5 | 5 MnO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) FeO | 10 | -10 | ([FeO])^(-10) H_2O | 1 | 1 | [H2O] K_2SO_4 | 1 | 1 | [K2SO4] Fe_2O_3 | 5 | 5 | ([Fe2O3])^5 MnO | 2 | 2 | ([MnO])^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 = ([H2SO4])^(-1) ([KMnO4])^(-2) ([FeO])^(-10) [H2O] [K2SO4] ([Fe2O3])^5 ([MnO])^2 = ([H2O] [K2SO4] ([Fe2O3])^5 ([MnO])^2)/([H2SO4] ([KMnO4])^2 ([FeO])^10)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + FeO ⟶ H_2O + K_2SO_4 + Fe_2O_3 + MnO 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: H_2SO_4 + 2 KMnO_4 + 10 FeO ⟶ H_2O + K_2SO_4 + 5 Fe_2O_3 + 2 MnO 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_2SO_4 | 1 | -1 KMnO_4 | 2 | -2 FeO | 10 | -10 H_2O | 1 | 1 K_2SO_4 | 1 | 1 Fe_2O_3 | 5 | 5 MnO | 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 H_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) FeO | 10 | -10 | -1/10 (Δ[FeO])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Fe_2O_3 | 5 | 5 | 1/5 (Δ[Fe2O3])/(Δt) MnO | 2 | 2 | 1/2 (Δ[MnO])/(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[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/10 (Δ[FeO])/(Δt) = (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/5 (Δ[Fe2O3])/(Δt) = 1/2 (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + FeO ⟶ H_2O + K_2SO_4 + Fe_2O_3 + MnO 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: H_2SO_4 + 2 KMnO_4 + 10 FeO ⟶ H_2O + K_2SO_4 + 5 Fe_2O_3 + 2 MnO 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_2SO_4 | 1 | -1 KMnO_4 | 2 | -2 FeO | 10 | -10 H_2O | 1 | 1 K_2SO_4 | 1 | 1 Fe_2O_3 | 5 | 5 MnO | 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 H_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) FeO | 10 | -10 | -1/10 (Δ[FeO])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Fe_2O_3 | 5 | 5 | 1/5 (Δ[Fe2O3])/(Δt) MnO | 2 | 2 | 1/2 (Δ[MnO])/(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[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/10 (Δ[FeO])/(Δt) = (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/5 (Δ[Fe2O3])/(Δt) = 1/2 (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | iron(II) oxide | water | potassium sulfate | iron(III) oxide | manganese monoxide formula | H_2SO_4 | KMnO_4 | FeO | H_2O | K_2SO_4 | Fe_2O_3 | MnO Hill formula | H_2O_4S | KMnO_4 | FeO | H_2O | K_2O_4S | Fe_2O_3 | MnO name | sulfuric acid | potassium permanganate | iron(II) oxide | water | potassium sulfate | iron(III) oxide | manganese monoxide IUPAC name | sulfuric acid | potassium permanganate | oxoiron | water | dipotassium sulfate | | oxomanganese
| sulfuric acid | potassium permanganate | iron(II) oxide | water | potassium sulfate | iron(III) oxide | manganese monoxide formula | H_2SO_4 | KMnO_4 | FeO | H_2O | K_2SO_4 | Fe_2O_3 | MnO Hill formula | H_2O_4S | KMnO_4 | FeO | H_2O | K_2O_4S | Fe_2O_3 | MnO name | sulfuric acid | potassium permanganate | iron(II) oxide | water | potassium sulfate | iron(III) oxide | manganese monoxide IUPAC name | sulfuric acid | potassium permanganate | oxoiron | water | dipotassium sulfate | | oxomanganese

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