NaOH + KMnO4 + H2O2 = H2O + O2 + KOH + Na2MnO4

NaOH sodium hydroxide + KMnO_4 potassium permanganate + H_2O_2 hydrogen peroxide ⟶ H_2O water + O_2 oxygen + KOH potassium hydroxide + Na2MnO4

Balance the chemical equation algebraically: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + Na2MnO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KMnO_4 + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 KOH + c_7 Na2MnO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, K and Mn: H: | c_1 + 2 c_3 = 2 c_4 + c_6 Na: | c_1 = 2 c_7 O: | c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + c_6 + 4 c_7 K: | c_2 = c_6 Mn: | c_2 = c_7 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/2 c_3 = 1 c_4 = c_1/4 + 1 c_5 = c_1/8 + 1/2 c_6 = c_1/2 c_7 = c_1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NaOH + 2 KMnO_4 + H_2O_2 ⟶ 2 H_2O + O_2 + 2 KOH + 2 Na2MnO4

+ + ⟶ + + + Na2MnO4

sodium hydroxide + potassium permanganate + hydrogen peroxide ⟶ water + oxygen + potassium hydroxide + Na2MnO4

Construct the equilibrium constant, K, expression for: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + Na2MnO4 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: 4 NaOH + 2 KMnO_4 + H_2O_2 ⟶ 2 H_2O + O_2 + 2 KOH + 2 Na2MnO4 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 NaOH | 4 | -4 KMnO_4 | 2 | -2 H_2O_2 | 1 | -1 H_2O | 2 | 2 O_2 | 1 | 1 KOH | 2 | 2 Na2MnO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 4 | -4 | ([NaOH])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 2 | 2 | ([H2O])^2 O_2 | 1 | 1 | [O2] KOH | 2 | 2 | ([KOH])^2 Na2MnO4 | 2 | 2 | ([Na2MnO4])^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 = ([NaOH])^(-4) ([KMnO4])^(-2) ([H2O2])^(-1) ([H2O])^2 [O2] ([KOH])^2 ([Na2MnO4])^2 = (([H2O])^2 [O2] ([KOH])^2 ([Na2MnO4])^2)/(([NaOH])^4 ([KMnO4])^2 [H2O2])

Construct the rate of reaction expression for: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + Na2MnO4 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: 4 NaOH + 2 KMnO_4 + H_2O_2 ⟶ 2 H_2O + O_2 + 2 KOH + 2 Na2MnO4 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 NaOH | 4 | -4 KMnO_4 | 2 | -2 H_2O_2 | 1 | -1 H_2O | 2 | 2 O_2 | 1 | 1 KOH | 2 | 2 Na2MnO4 | 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 NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) Na2MnO4 | 2 | 2 | 1/2 (Δ[Na2MnO4])/(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 = -1/4 (Δ[NaOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[H2O2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[Na2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | Na2MnO4 formula | NaOH | KMnO_4 | H_2O_2 | H_2O | O_2 | KOH | Na2MnO4 Hill formula | HNaO | KMnO_4 | H_2O_2 | H_2O | O_2 | HKO | MnNa2O4 name | sodium hydroxide | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | IUPAC name | sodium hydroxide | potassium permanganate | hydrogen peroxide | water | molecular oxygen | potassium hydroxide |

| sodium hydroxide | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | Na2MnO4 molar mass | 39.997 g/mol | 158.03 g/mol | 34.014 g/mol | 18.015 g/mol | 31.998 g/mol | 56.105 g/mol | 164.91 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | melting point | 323 °C | 240 °C | -0.43 °C | 0 °C | -218 °C | 406 °C | boiling point | 1390 °C | | 150.2 °C | 99.9839 °C | -183 °C | 1327 °C | density | 2.13 g/cm^3 | 1 g/cm^3 | 1.44 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 2.044 g/cm^3 | solubility in water | soluble | | miscible | | | soluble | surface tension | 0.07435 N/m | | 0.0804 N/m | 0.0728 N/m | 0.01347 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 0.001249 Pa s (at 20 °C) | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | odor | | odorless | | odorless | odorless | |