KOH + Pb + KNO2 = H2O + NH3 + K2PbO2

KOH potassium hydroxide + Pb lead + KNO_2 potassium nitrite ⟶ H_2O water + NH_3 ammonia + K2PbO2

Balance the chemical equation algebraically: KOH + Pb + KNO_2 ⟶ H_2O + NH_3 + K2PbO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Pb + c_3 KNO_2 ⟶ c_4 H_2O + c_5 NH_3 + c_6 K2PbO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Pb and N: H: | c_1 = 2 c_4 + 3 c_5 K: | c_1 + c_3 = 2 c_6 O: | c_1 + 2 c_3 = c_4 + 2 c_6 Pb: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 3 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 KOH + 3 Pb + KNO_2 ⟶ H_2O + NH_3 + 3 K2PbO2

+ + ⟶ + + K2PbO2

potassium hydroxide + lead + potassium nitrite ⟶ water + ammonia + K2PbO2

Construct the equilibrium constant, K, expression for: KOH + Pb + KNO_2 ⟶ H_2O + NH_3 + K2PbO2 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: 5 KOH + 3 Pb + KNO_2 ⟶ H_2O + NH_3 + 3 K2PbO2 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 | 5 | -5 Pb | 3 | -3 KNO_2 | 1 | -1 H_2O | 1 | 1 NH_3 | 1 | 1 K2PbO2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 5 | -5 | ([KOH])^(-5) Pb | 3 | -3 | ([Pb])^(-3) KNO_2 | 1 | -1 | ([KNO2])^(-1) H_2O | 1 | 1 | [H2O] NH_3 | 1 | 1 | [NH3] K2PbO2 | 3 | 3 | ([K2PbO2])^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 = ([KOH])^(-5) ([Pb])^(-3) ([KNO2])^(-1) [H2O] [NH3] ([K2PbO2])^3 = ([H2O] [NH3] ([K2PbO2])^3)/(([KOH])^5 ([Pb])^3 [KNO2])

Construct the rate of reaction expression for: KOH + Pb + KNO_2 ⟶ H_2O + NH_3 + K2PbO2 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: 5 KOH + 3 Pb + KNO_2 ⟶ H_2O + NH_3 + 3 K2PbO2 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 | 5 | -5 Pb | 3 | -3 KNO_2 | 1 | -1 H_2O | 1 | 1 NH_3 | 1 | 1 K2PbO2 | 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 KOH | 5 | -5 | -1/5 (Δ[KOH])/(Δt) Pb | 3 | -3 | -1/3 (Δ[Pb])/(Δt) KNO_2 | 1 | -1 | -(Δ[KNO2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(Δt) K2PbO2 | 3 | 3 | 1/3 (Δ[K2PbO2])/(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 = -1/5 (Δ[KOH])/(Δt) = -1/3 (Δ[Pb])/(Δt) = -(Δ[KNO2])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NH3])/(Δt) = 1/3 (Δ[K2PbO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | lead | potassium nitrite | water | ammonia | K2PbO2 formula | KOH | Pb | KNO_2 | H_2O | NH_3 | K2PbO2 Hill formula | HKO | Pb | KNO_2 | H_2O | H_3N | K2O2Pb name | potassium hydroxide | lead | potassium nitrite | water | ammonia |

| potassium hydroxide | lead | potassium nitrite | water | ammonia | K2PbO2 molar mass | 56.105 g/mol | 207.2 g/mol | 85.103 g/mol | 18.015 g/mol | 17.031 g/mol | 317.4 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | 406 °C | 327.4 °C | 350 °C | 0 °C | -77.73 °C | boiling point | 1327 °C | 1740 °C | | 99.9839 °C | -33.33 °C | density | 2.044 g/cm^3 | 11.34 g/cm^3 | 1.915 g/cm^3 | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | solubility in water | soluble | insoluble | | | | surface tension | | | | 0.0728 N/m | 0.0234 N/m | dynamic viscosity | 0.001 Pa s (at 550 °C) | 0.00183 Pa s (at 38 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | odor | | | | odorless | |