H2O + KNO2 + NaMnO4 = NaOH + MnO2 + KNO3

H_2O water + KNO_2 potassium nitrite + NaMnO_4 sodium permanganate ⟶ NaOH sodium hydroxide + MnO_2 manganese dioxide + KNO_3 potassium nitrate

Balance the chemical equation algebraically: H_2O + KNO_2 + NaMnO_4 ⟶ NaOH + MnO_2 + KNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KNO_2 + c_3 NaMnO_4 ⟶ c_4 NaOH + c_5 MnO_2 + c_6 KNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, N, Mn and Na: H: | 2 c_1 = c_4 O: | c_1 + 2 c_2 + 4 c_3 = c_4 + 2 c_5 + 3 c_6 K: | c_2 = c_6 N: | c_2 = c_6 Mn: | c_3 = c_5 Na: | 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 = 3 c_3 = 2 c_4 = 2 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 3 KNO_2 + 2 NaMnO_4 ⟶ 2 NaOH + 2 MnO_2 + 3 KNO_3

+ + ⟶ + +

water + potassium nitrite + sodium permanganate ⟶ sodium hydroxide + manganese dioxide + potassium nitrate

Construct the equilibrium constant, K, expression for: H_2O + KNO_2 + NaMnO_4 ⟶ NaOH + MnO_2 + KNO_3 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_2O + 3 KNO_2 + 2 NaMnO_4 ⟶ 2 NaOH + 2 MnO_2 + 3 KNO_3 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 | 1 | -1 KNO_2 | 3 | -3 NaMnO_4 | 2 | -2 NaOH | 2 | 2 MnO_2 | 2 | 2 KNO_3 | 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 | 1 | -1 | ([H2O])^(-1) KNO_2 | 3 | -3 | ([KNO2])^(-3) NaMnO_4 | 2 | -2 | ([NaMnO4])^(-2) NaOH | 2 | 2 | ([NaOH])^2 MnO_2 | 2 | 2 | ([MnO2])^2 KNO_3 | 3 | 3 | ([KNO3])^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])^(-1) ([KNO2])^(-3) ([NaMnO4])^(-2) ([NaOH])^2 ([MnO2])^2 ([KNO3])^3 = (([NaOH])^2 ([MnO2])^2 ([KNO3])^3)/([H2O] ([KNO2])^3 ([NaMnO4])^2)

Construct the rate of reaction expression for: H_2O + KNO_2 + NaMnO_4 ⟶ NaOH + MnO_2 + KNO_3 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_2O + 3 KNO_2 + 2 NaMnO_4 ⟶ 2 NaOH + 2 MnO_2 + 3 KNO_3 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 | 1 | -1 KNO_2 | 3 | -3 NaMnO_4 | 2 | -2 NaOH | 2 | 2 MnO_2 | 2 | 2 KNO_3 | 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 | 1 | -1 | -(Δ[H2O])/(Δt) KNO_2 | 3 | -3 | -1/3 (Δ[KNO2])/(Δt) NaMnO_4 | 2 | -2 | -1/2 (Δ[NaMnO4])/(Δt) NaOH | 2 | 2 | 1/2 (Δ[NaOH])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) KNO_3 | 3 | 3 | 1/3 (Δ[KNO3])/(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[H2O])/(Δt) = -1/3 (Δ[KNO2])/(Δt) = -1/2 (Δ[NaMnO4])/(Δt) = 1/2 (Δ[NaOH])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = 1/3 (Δ[KNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium nitrite | sodium permanganate | sodium hydroxide | manganese dioxide | potassium nitrate formula | H_2O | KNO_2 | NaMnO_4 | NaOH | MnO_2 | KNO_3 Hill formula | H_2O | KNO_2 | MnNaO_4 | HNaO | MnO_2 | KNO_3 name | water | potassium nitrite | sodium permanganate | sodium hydroxide | manganese dioxide | potassium nitrate IUPAC name | water | potassium nitrite | sodium permanganate | sodium hydroxide | dioxomanganese | potassium nitrate

| water | potassium nitrite | sodium permanganate | sodium hydroxide | manganese dioxide | potassium nitrate molar mass | 18.015 g/mol | 85.103 g/mol | 141.92 g/mol | 39.997 g/mol | 86.936 g/mol | 101.1 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | 350 °C | | 323 °C | 535 °C | 334 °C boiling point | 99.9839 °C | | 100 °C | 1390 °C | | density | 1 g/cm^3 | 1.915 g/cm^3 | 1.391 g/cm^3 | 2.13 g/cm^3 | 5.03 g/cm^3 | solubility in water | | | | soluble | insoluble | soluble surface tension | 0.0728 N/m | | | 0.07435 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.004 Pa s (at 350 °C) | | odor | odorless | | | | | odorless