KOH + PbO2 + KCrO2 = H2O + K2CrO4 + K2PbO2

KOH potassium hydroxide + PbO_2 lead dioxide + KCrO2 ⟶ H_2O water + K_2CrO_4 potassium chromate + K2PbO2

Balance the chemical equation algebraically: KOH + PbO_2 + KCrO2 ⟶ H_2O + K_2CrO_4 + K2PbO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 PbO_2 + c_3 KCrO2 ⟶ c_4 H_2O + c_5 K_2CrO_4 + 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 Cr: H: | c_1 = 2 c_4 K: | c_1 + c_3 = 2 c_5 + 2 c_6 O: | c_1 + 2 c_2 + 2 c_3 = c_4 + 4 c_5 + 2 c_6 Pb: | c_2 = c_6 Cr: | 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 = 4 c_2 = 3/2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 4 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KOH + 3 PbO_2 + 2 KCrO2 ⟶ 4 H_2O + 2 K_2CrO_4 + 3 K2PbO2

+ + KCrO2 ⟶ + + K2PbO2

potassium hydroxide + lead dioxide + KCrO2 ⟶ water + potassium chromate + K2PbO2

Construct the equilibrium constant, K, expression for: KOH + PbO_2 + KCrO2 ⟶ H_2O + K_2CrO_4 + 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: 8 KOH + 3 PbO_2 + 2 KCrO2 ⟶ 4 H_2O + 2 K_2CrO_4 + 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 | 8 | -8 PbO_2 | 3 | -3 KCrO2 | 2 | -2 H_2O | 4 | 4 K_2CrO_4 | 2 | 2 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 | 8 | -8 | ([KOH])^(-8) PbO_2 | 3 | -3 | ([PbO2])^(-3) KCrO2 | 2 | -2 | ([KCrO2])^(-2) H_2O | 4 | 4 | ([H2O])^4 K_2CrO_4 | 2 | 2 | ([K2CrO4])^2 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])^(-8) ([PbO2])^(-3) ([KCrO2])^(-2) ([H2O])^4 ([K2CrO4])^2 ([K2PbO2])^3 = (([H2O])^4 ([K2CrO4])^2 ([K2PbO2])^3)/(([KOH])^8 ([PbO2])^3 ([KCrO2])^2)

Construct the rate of reaction expression for: KOH + PbO_2 + KCrO2 ⟶ H_2O + K_2CrO_4 + 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: 8 KOH + 3 PbO_2 + 2 KCrO2 ⟶ 4 H_2O + 2 K_2CrO_4 + 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 | 8 | -8 PbO_2 | 3 | -3 KCrO2 | 2 | -2 H_2O | 4 | 4 K_2CrO_4 | 2 | 2 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 | 8 | -8 | -1/8 (Δ[KOH])/(Δt) PbO_2 | 3 | -3 | -1/3 (Δ[PbO2])/(Δt) KCrO2 | 2 | -2 | -1/2 (Δ[KCrO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(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 = -1/8 (Δ[KOH])/(Δt) = -1/3 (Δ[PbO2])/(Δt) = -1/2 (Δ[KCrO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) = 1/3 (Δ[K2PbO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | lead dioxide | KCrO2 | water | potassium chromate | K2PbO2 formula | KOH | PbO_2 | KCrO2 | H_2O | K_2CrO_4 | K2PbO2 Hill formula | HKO | O_2Pb | CrKO2 | H_2O | CrK_2O_4 | K2O2Pb name | potassium hydroxide | lead dioxide | | water | potassium chromate | IUPAC name | potassium hydroxide | | | water | dipotassium dioxido-dioxochromium |

| potassium hydroxide | lead dioxide | KCrO2 | water | potassium chromate | K2PbO2 molar mass | 56.105 g/mol | 239.2 g/mol | 123.09 g/mol | 18.015 g/mol | 194.19 g/mol | 317.4 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 406 °C | 290 °C | | 0 °C | 971 °C | boiling point | 1327 °C | | | 99.9839 °C | | density | 2.044 g/cm^3 | 9.58 g/cm^3 | | 1 g/cm^3 | 2.73 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 |