KOH + Fe + KNO3 = H2O + KNO2 + K2FeO4

KOH potassium hydroxide + Fe iron + KNO_3 potassium nitrate ⟶ H_2O water + KNO_2 potassium nitrite + K_2FeO_4 potassium ferrate(VI)

Balance the chemical equation algebraically: KOH + Fe + KNO_3 ⟶ H_2O + KNO_2 + K_2FeO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Fe + c_3 KNO_3 ⟶ c_4 H_2O + c_5 KNO_2 + c_6 K_2FeO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Fe and N: H: | c_1 = 2 c_4 K: | c_1 + c_3 = c_5 + c_6 O: | c_1 + 3 c_3 = c_4 + 2 c_5 + 2 c_6 Fe: | c_2 = c_6 N: | c_3 = 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 = 3 c_4 = 1 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 Fe + 3 KNO_3 ⟶ H_2O + 3 KNO_2 + 2 K_2FeO_4

+ + ⟶ + +

potassium hydroxide + iron + potassium nitrate ⟶ water + potassium nitrite + potassium ferrate(VI)

Construct the equilibrium constant, K, expression for: KOH + Fe + KNO_3 ⟶ H_2O + KNO_2 + K_2FeO_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: 2 KOH + 2 Fe + 3 KNO_3 ⟶ H_2O + 3 KNO_2 + 2 K_2FeO_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 | 2 | -2 Fe | 2 | -2 KNO_3 | 3 | -3 H_2O | 1 | 1 KNO_2 | 3 | 3 K_2FeO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) Fe | 2 | -2 | ([Fe])^(-2) KNO_3 | 3 | -3 | ([KNO3])^(-3) H_2O | 1 | 1 | [H2O] KNO_2 | 3 | 3 | ([KNO2])^3 K_2FeO_4 | 2 | 2 | ([K2FeO4])^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 = ([KOH])^(-2) ([Fe])^(-2) ([KNO3])^(-3) [H2O] ([KNO2])^3 ([K2FeO4])^2 = ([H2O] ([KNO2])^3 ([K2FeO4])^2)/(([KOH])^2 ([Fe])^2 ([KNO3])^3)

Construct the rate of reaction expression for: KOH + Fe + KNO_3 ⟶ H_2O + KNO_2 + K_2FeO_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: 2 KOH + 2 Fe + 3 KNO_3 ⟶ H_2O + 3 KNO_2 + 2 K_2FeO_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 | 2 | -2 Fe | 2 | -2 KNO_3 | 3 | -3 H_2O | 1 | 1 KNO_2 | 3 | 3 K_2FeO_4 | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) Fe | 2 | -2 | -1/2 (Δ[Fe])/(Δt) KNO_3 | 3 | -3 | -1/3 (Δ[KNO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KNO_2 | 3 | 3 | 1/3 (Δ[KNO2])/(Δt) K_2FeO_4 | 2 | 2 | 1/2 (Δ[K2FeO4])/(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[KOH])/(Δt) = -1/2 (Δ[Fe])/(Δt) = -1/3 (Δ[KNO3])/(Δt) = (Δ[H2O])/(Δt) = 1/3 (Δ[KNO2])/(Δt) = 1/2 (Δ[K2FeO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | iron | potassium nitrate | water | potassium nitrite | potassium ferrate(VI) formula | KOH | Fe | KNO_3 | H_2O | KNO_2 | K_2FeO_4 Hill formula | HKO | Fe | KNO_3 | H_2O | KNO_2 | FeK_2O_4 name | potassium hydroxide | iron | potassium nitrate | water | potassium nitrite | potassium ferrate(VI)

| potassium hydroxide | iron | potassium nitrate | water | potassium nitrite | potassium ferrate(VI) molar mass | 56.105 g/mol | 55.845 g/mol | 101.1 g/mol | 18.015 g/mol | 85.103 g/mol | 126.94 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 1535 °C | 334 °C | 0 °C | 350 °C | 400 °C boiling point | 1327 °C | 2750 °C | | 99.9839 °C | | density | 2.044 g/cm^3 | 7.874 g/cm^3 | | 1 g/cm^3 | 1.915 g/cm^3 | solubility in water | soluble | insoluble | soluble | | | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | odorless | |