KOH + KMnO4 + NH3 = H2O + N2 + K2MnO4

KOH potassium hydroxide + KMnO_4 potassium permanganate + NH_3 ammonia ⟶ H_2O water + N_2 nitrogen + K_2MnO_4 potassium manganate

Balance the chemical equation algebraically: KOH + KMnO_4 + NH_3 ⟶ H_2O + N_2 + K_2MnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 NH_3 ⟶ c_4 H_2O + c_5 N_2 + c_6 K_2MnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn and N: H: | c_1 + 3 c_3 = 2 c_4 K: | c_1 + c_2 = 2 c_6 O: | c_1 + 4 c_2 = c_4 + 4 c_6 Mn: | c_2 = c_6 N: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 6 c_3 = 2 c_4 = 6 c_5 = 1 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 KOH + 6 KMnO_4 + 2 NH_3 ⟶ 6 H_2O + N_2 + 6 K_2MnO_4

+ + ⟶ + +

potassium hydroxide + potassium permanganate + ammonia ⟶ water + nitrogen + potassium manganate

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + NH_3 ⟶ H_2O + N_2 + K_2MnO_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: 6 KOH + 6 KMnO_4 + 2 NH_3 ⟶ 6 H_2O + N_2 + 6 K_2MnO_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 KOH | 6 | -6 KMnO_4 | 6 | -6 NH_3 | 2 | -2 H_2O | 6 | 6 N_2 | 1 | 1 K_2MnO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 6 | -6 | ([KOH])^(-6) KMnO_4 | 6 | -6 | ([KMnO4])^(-6) NH_3 | 2 | -2 | ([NH3])^(-2) H_2O | 6 | 6 | ([H2O])^6 N_2 | 1 | 1 | [N2] K_2MnO_4 | 6 | 6 | ([K2MnO4])^6 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 = ([KOH])^(-6) ([KMnO4])^(-6) ([NH3])^(-2) ([H2O])^6 [N2] ([K2MnO4])^6 = (([H2O])^6 [N2] ([K2MnO4])^6)/(([KOH])^6 ([KMnO4])^6 ([NH3])^2)

Construct the rate of reaction expression for: KOH + KMnO_4 + NH_3 ⟶ H_2O + N_2 + K_2MnO_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: 6 KOH + 6 KMnO_4 + 2 NH_3 ⟶ 6 H_2O + N_2 + 6 K_2MnO_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 KOH | 6 | -6 KMnO_4 | 6 | -6 NH_3 | 2 | -2 H_2O | 6 | 6 N_2 | 1 | 1 K_2MnO_4 | 6 | 6 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 KOH | 6 | -6 | -1/6 (Δ[KOH])/(Δt) KMnO_4 | 6 | -6 | -1/6 (Δ[KMnO4])/(Δt) NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) K_2MnO_4 | 6 | 6 | 1/6 (Δ[K2MnO4])/(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 = -1/6 (Δ[KOH])/(Δt) = -1/6 (Δ[KMnO4])/(Δt) = -1/2 (Δ[NH3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[N2])/(Δt) = 1/6 (Δ[K2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium permanganate | ammonia | water | nitrogen | potassium manganate formula | KOH | KMnO_4 | NH_3 | H_2O | N_2 | K_2MnO_4 Hill formula | HKO | KMnO_4 | H_3N | H_2O | N_2 | K_2MnO_4 name | potassium hydroxide | potassium permanganate | ammonia | water | nitrogen | potassium manganate IUPAC name | potassium hydroxide | potassium permanganate | ammonia | water | molecular nitrogen | dipotassium dioxido-dioxomanganese

| potassium hydroxide | potassium permanganate | ammonia | water | nitrogen | potassium manganate molar mass | 56.105 g/mol | 158.03 g/mol | 17.031 g/mol | 18.015 g/mol | 28.014 g/mol | 197.13 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 406 °C | 240 °C | -77.73 °C | 0 °C | -210 °C | 190 °C boiling point | 1327 °C | | -33.33 °C | 99.9839 °C | -195.79 °C | density | 2.044 g/cm^3 | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 1 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | solubility in water | soluble | | | | insoluble | decomposes surface tension | | | 0.0234 N/m | 0.0728 N/m | 0.0066 N/m | dynamic viscosity | 0.001 Pa s (at 550 °C) | | 1.009×10^-5 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | | odorless | | odorless | odorless |