KMnO4 + NaNO2 = NO2 + K2MnO4 + Na2MnO4

KMnO_4 potassium permanganate + NaNO_2 sodium nitrite ⟶ NO_2 nitrogen dioxide + K_2MnO_4 potassium manganate + Na2MnO4

Balance the chemical equation algebraically: KMnO_4 + NaNO_2 ⟶ NO_2 + K_2MnO_4 + Na2MnO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 NaNO_2 ⟶ c_3 NO_2 + c_4 K_2MnO_4 + c_5 Na2MnO4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, N and Na: K: | c_1 = 2 c_4 Mn: | c_1 = c_4 + c_5 O: | 4 c_1 + 2 c_2 = 2 c_3 + 4 c_4 + 4 c_5 N: | c_2 = c_3 Na: | c_2 = 2 c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + 2 NaNO_2 ⟶ 2 NO_2 + K_2MnO_4 + Na2MnO4

+ ⟶ + + Na2MnO4

potassium permanganate + sodium nitrite ⟶ nitrogen dioxide + potassium manganate + Na2MnO4

Construct the equilibrium constant, K, expression for: KMnO_4 + NaNO_2 ⟶ NO_2 + K_2MnO_4 + 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: 2 KMnO_4 + 2 NaNO_2 ⟶ 2 NO_2 + K_2MnO_4 + 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 KMnO_4 | 2 | -2 NaNO_2 | 2 | -2 NO_2 | 2 | 2 K_2MnO_4 | 1 | 1 Na2MnO4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 2 | -2 | ([KMnO4])^(-2) NaNO_2 | 2 | -2 | ([NaNO2])^(-2) NO_2 | 2 | 2 | ([NO2])^2 K_2MnO_4 | 1 | 1 | [K2MnO4] Na2MnO4 | 1 | 1 | [Na2MnO4] 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 = ([KMnO4])^(-2) ([NaNO2])^(-2) ([NO2])^2 [K2MnO4] [Na2MnO4] = (([NO2])^2 [K2MnO4] [Na2MnO4])/(([KMnO4])^2 ([NaNO2])^2)

Construct the rate of reaction expression for: KMnO_4 + NaNO_2 ⟶ NO_2 + K_2MnO_4 + 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: 2 KMnO_4 + 2 NaNO_2 ⟶ 2 NO_2 + K_2MnO_4 + 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 KMnO_4 | 2 | -2 NaNO_2 | 2 | -2 NO_2 | 2 | 2 K_2MnO_4 | 1 | 1 Na2MnO4 | 1 | 1 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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) NaNO_2 | 2 | -2 | -1/2 (Δ[NaNO2])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) K_2MnO_4 | 1 | 1 | (Δ[K2MnO4])/(Δt) Na2MnO4 | 1 | 1 | (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 = -1/2 (Δ[KMnO4])/(Δt) = -1/2 (Δ[NaNO2])/(Δt) = 1/2 (Δ[NO2])/(Δt) = (Δ[K2MnO4])/(Δt) = (Δ[Na2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | sodium nitrite | nitrogen dioxide | potassium manganate | Na2MnO4 formula | KMnO_4 | NaNO_2 | NO_2 | K_2MnO_4 | Na2MnO4 Hill formula | KMnO_4 | NNaO_2 | NO_2 | K_2MnO_4 | MnNa2O4 name | potassium permanganate | sodium nitrite | nitrogen dioxide | potassium manganate | IUPAC name | potassium permanganate | sodium nitrite | Nitrogen dioxide | dipotassium dioxido-dioxomanganese |

| potassium permanganate | sodium nitrite | nitrogen dioxide | potassium manganate | Na2MnO4 molar mass | 158.03 g/mol | 68.995 g/mol | 46.005 g/mol | 197.13 g/mol | 164.91 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | melting point | 240 °C | 271 °C | -11 °C | 190 °C | boiling point | | | 21 °C | | density | 1 g/cm^3 | 2.168 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | | solubility in water | | | reacts | decomposes | dynamic viscosity | | | 4.02×10^-4 Pa s (at 25 °C) | | odor | odorless | | | |