NaOH + K2MnO4 = KOH + Na2MnO4

NaOH sodium hydroxide + K_2MnO_4 potassium manganate ⟶ KOH potassium hydroxide + Na2MnO4

Balance the chemical equation algebraically: NaOH + K_2MnO_4 ⟶ KOH + Na2MnO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 K_2MnO_4 ⟶ c_3 KOH + c_4 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 = c_3 Na: | c_1 = 2 c_4 O: | c_1 + 4 c_2 = c_3 + 4 c_4 K: | 2 c_2 = c_3 Mn: | c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + K_2MnO_4 ⟶ 2 KOH + Na2MnO4

+ ⟶ + Na2MnO4

sodium hydroxide + potassium manganate ⟶ potassium hydroxide + Na2MnO4

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

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

| sodium hydroxide | potassium manganate | potassium hydroxide | Na2MnO4 formula | NaOH | K_2MnO_4 | KOH | Na2MnO4 Hill formula | HNaO | K_2MnO_4 | HKO | MnNa2O4 name | sodium hydroxide | potassium manganate | potassium hydroxide | IUPAC name | sodium hydroxide | dipotassium dioxido-dioxomanganese | potassium hydroxide |

| sodium hydroxide | potassium manganate | potassium hydroxide | Na2MnO4 molar mass | 39.997 g/mol | 197.13 g/mol | 56.105 g/mol | 164.91 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 323 °C | 190 °C | 406 °C | boiling point | 1390 °C | | 1327 °C | density | 2.13 g/cm^3 | | 2.044 g/cm^3 | solubility in water | soluble | decomposes | soluble | surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 0.001 Pa s (at 550 °C) |