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H2O + KMnO4 + NaClO2 = KOH + MnO2 + NaClO4

Input interpretation

H_2O water + KMnO_4 potassium permanganate + NaClO_2 sodium chlorite ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + NaClO_4 sodium perchlorate
H_2O water + KMnO_4 potassium permanganate + NaClO_2 sodium chlorite ⟶ KOH potassium hydroxide + MnO_2 manganese dioxide + NaClO_4 sodium perchlorate

Balanced equation

Balance the chemical equation algebraically: H_2O + KMnO_4 + NaClO_2 ⟶ KOH + MnO_2 + NaClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 NaClO_2 ⟶ c_4 KOH + c_5 MnO_2 + c_6 NaClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn, Cl and Na: H: | 2 c_1 = c_4 O: | c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + 4 c_6 K: | c_2 = c_4 Mn: | c_2 = c_5 Cl: | c_3 = c_6 Na: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 3/2 c_4 = 2 c_5 = 2 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 4 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 4 KMnO_4 + 3 NaClO_2 ⟶ 4 KOH + 4 MnO_2 + 3 NaClO_4
Balance the chemical equation algebraically: H_2O + KMnO_4 + NaClO_2 ⟶ KOH + MnO_2 + NaClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 NaClO_2 ⟶ c_4 KOH + c_5 MnO_2 + c_6 NaClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn, Cl and Na: H: | 2 c_1 = c_4 O: | c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + 4 c_6 K: | c_2 = c_4 Mn: | c_2 = c_5 Cl: | c_3 = c_6 Na: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 3/2 c_4 = 2 c_5 = 2 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 4 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 4 KMnO_4 + 3 NaClO_2 ⟶ 4 KOH + 4 MnO_2 + 3 NaClO_4

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + potassium permanganate + sodium chlorite ⟶ potassium hydroxide + manganese dioxide + sodium perchlorate
water + potassium permanganate + sodium chlorite ⟶ potassium hydroxide + manganese dioxide + sodium perchlorate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + NaClO_2 ⟶ KOH + MnO_2 + NaClO_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: 2 H_2O + 4 KMnO_4 + 3 NaClO_2 ⟶ 4 KOH + 4 MnO_2 + 3 NaClO_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 H_2O | 2 | -2 KMnO_4 | 4 | -4 NaClO_2 | 3 | -3 KOH | 4 | 4 MnO_2 | 4 | 4 NaClO_4 | 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 | 4 | -4 | ([KMnO4])^(-4) NaClO_2 | 3 | -3 | ([NaClO2])^(-3) KOH | 4 | 4 | ([KOH])^4 MnO_2 | 4 | 4 | ([MnO2])^4 NaClO_4 | 3 | 3 | ([NaClO4])^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])^(-4) ([NaClO2])^(-3) ([KOH])^4 ([MnO2])^4 ([NaClO4])^3 = (([KOH])^4 ([MnO2])^4 ([NaClO4])^3)/(([H2O])^2 ([KMnO4])^4 ([NaClO2])^3)
Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + NaClO_2 ⟶ KOH + MnO_2 + NaClO_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: 2 H_2O + 4 KMnO_4 + 3 NaClO_2 ⟶ 4 KOH + 4 MnO_2 + 3 NaClO_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 H_2O | 2 | -2 KMnO_4 | 4 | -4 NaClO_2 | 3 | -3 KOH | 4 | 4 MnO_2 | 4 | 4 NaClO_4 | 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 | 4 | -4 | ([KMnO4])^(-4) NaClO_2 | 3 | -3 | ([NaClO2])^(-3) KOH | 4 | 4 | ([KOH])^4 MnO_2 | 4 | 4 | ([MnO2])^4 NaClO_4 | 3 | 3 | ([NaClO4])^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])^(-4) ([NaClO2])^(-3) ([KOH])^4 ([MnO2])^4 ([NaClO4])^3 = (([KOH])^4 ([MnO2])^4 ([NaClO4])^3)/(([H2O])^2 ([KMnO4])^4 ([NaClO2])^3)

Rate of reaction

Construct the rate of reaction expression for: H_2O + KMnO_4 + NaClO_2 ⟶ KOH + MnO_2 + NaClO_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: 2 H_2O + 4 KMnO_4 + 3 NaClO_2 ⟶ 4 KOH + 4 MnO_2 + 3 NaClO_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 H_2O | 2 | -2 KMnO_4 | 4 | -4 NaClO_2 | 3 | -3 KOH | 4 | 4 MnO_2 | 4 | 4 NaClO_4 | 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 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) NaClO_2 | 3 | -3 | -1/3 (Δ[NaClO2])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(Δt) NaClO_4 | 3 | 3 | 1/3 (Δ[NaClO4])/(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) = -1/4 (Δ[KMnO4])/(Δt) = -1/3 (Δ[NaClO2])/(Δt) = 1/4 (Δ[KOH])/(Δt) = 1/4 (Δ[MnO2])/(Δt) = 1/3 (Δ[NaClO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + KMnO_4 + NaClO_2 ⟶ KOH + MnO_2 + NaClO_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: 2 H_2O + 4 KMnO_4 + 3 NaClO_2 ⟶ 4 KOH + 4 MnO_2 + 3 NaClO_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 H_2O | 2 | -2 KMnO_4 | 4 | -4 NaClO_2 | 3 | -3 KOH | 4 | 4 MnO_2 | 4 | 4 NaClO_4 | 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 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) NaClO_2 | 3 | -3 | -1/3 (Δ[NaClO2])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(Δt) NaClO_4 | 3 | 3 | 1/3 (Δ[NaClO4])/(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) = -1/4 (Δ[KMnO4])/(Δt) = -1/3 (Δ[NaClO2])/(Δt) = 1/4 (Δ[KOH])/(Δt) = 1/4 (Δ[MnO2])/(Δt) = 1/3 (Δ[NaClO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | potassium permanganate | sodium chlorite | potassium hydroxide | manganese dioxide | sodium perchlorate formula | H_2O | KMnO_4 | NaClO_2 | KOH | MnO_2 | NaClO_4 Hill formula | H_2O | KMnO_4 | ClNaO_2 | HKO | MnO_2 | ClNaO_4 name | water | potassium permanganate | sodium chlorite | potassium hydroxide | manganese dioxide | sodium perchlorate IUPAC name | water | potassium permanganate | | potassium hydroxide | dioxomanganese | sodium perchlorate
| water | potassium permanganate | sodium chlorite | potassium hydroxide | manganese dioxide | sodium perchlorate formula | H_2O | KMnO_4 | NaClO_2 | KOH | MnO_2 | NaClO_4 Hill formula | H_2O | KMnO_4 | ClNaO_2 | HKO | MnO_2 | ClNaO_4 name | water | potassium permanganate | sodium chlorite | potassium hydroxide | manganese dioxide | sodium perchlorate IUPAC name | water | potassium permanganate | | potassium hydroxide | dioxomanganese | sodium perchlorate

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