NaOH + PbO2 + NaCrO2 = H2O + Na2CrO4 + Na2PbO2

NaOH sodium hydroxide + PbO_2 lead dioxide + NaCrO2 ⟶ H_2O water + Na_2CrO_4 sodium chromate + Na2PbO2

Balance the chemical equation algebraically: NaOH + PbO_2 + NaCrO2 ⟶ H_2O + Na_2CrO_4 + Na2PbO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 PbO_2 + c_3 NaCrO2 ⟶ c_4 H_2O + c_5 Na_2CrO_4 + c_6 Na2PbO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Pb and Cr: H: | c_1 = 2 c_4 Na: | 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 NaOH + 3 PbO_2 + 2 NaCrO2 ⟶ 4 H_2O + 2 Na_2CrO_4 + 3 Na2PbO2

+ + NaCrO2 ⟶ + + Na2PbO2

sodium hydroxide + lead dioxide + NaCrO2 ⟶ water + sodium chromate + Na2PbO2

Construct the equilibrium constant, K, expression for: NaOH + PbO_2 + NaCrO2 ⟶ H_2O + Na_2CrO_4 + Na2PbO2 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 NaOH + 3 PbO_2 + 2 NaCrO2 ⟶ 4 H_2O + 2 Na_2CrO_4 + 3 Na2PbO2 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 | 8 | -8 PbO_2 | 3 | -3 NaCrO2 | 2 | -2 H_2O | 4 | 4 Na_2CrO_4 | 2 | 2 Na2PbO2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 8 | -8 | ([NaOH])^(-8) PbO_2 | 3 | -3 | ([PbO2])^(-3) NaCrO2 | 2 | -2 | ([NaCrO2])^(-2) H_2O | 4 | 4 | ([H2O])^4 Na_2CrO_4 | 2 | 2 | ([Na2CrO4])^2 Na2PbO2 | 3 | 3 | ([Na2PbO2])^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 = ([NaOH])^(-8) ([PbO2])^(-3) ([NaCrO2])^(-2) ([H2O])^4 ([Na2CrO4])^2 ([Na2PbO2])^3 = (([H2O])^4 ([Na2CrO4])^2 ([Na2PbO2])^3)/(([NaOH])^8 ([PbO2])^3 ([NaCrO2])^2)

Construct the rate of reaction expression for: NaOH + PbO_2 + NaCrO2 ⟶ H_2O + Na_2CrO_4 + Na2PbO2 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 NaOH + 3 PbO_2 + 2 NaCrO2 ⟶ 4 H_2O + 2 Na_2CrO_4 + 3 Na2PbO2 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 | 8 | -8 PbO_2 | 3 | -3 NaCrO2 | 2 | -2 H_2O | 4 | 4 Na_2CrO_4 | 2 | 2 Na2PbO2 | 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 NaOH | 8 | -8 | -1/8 (Δ[NaOH])/(Δt) PbO_2 | 3 | -3 | -1/3 (Δ[PbO2])/(Δt) NaCrO2 | 2 | -2 | -1/2 (Δ[NaCrO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Na_2CrO_4 | 2 | 2 | 1/2 (Δ[Na2CrO4])/(Δt) Na2PbO2 | 3 | 3 | 1/3 (Δ[Na2PbO2])/(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[NaOH])/(Δt) = -1/3 (Δ[PbO2])/(Δt) = -1/2 (Δ[NaCrO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) = 1/3 (Δ[Na2PbO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | lead dioxide | NaCrO2 | water | sodium chromate | Na2PbO2 formula | NaOH | PbO_2 | NaCrO2 | H_2O | Na_2CrO_4 | Na2PbO2 Hill formula | HNaO | O_2Pb | CrNaO2 | H_2O | CrNa_2O_4 | Na2O2Pb name | sodium hydroxide | lead dioxide | | water | sodium chromate | IUPAC name | sodium hydroxide | | | water | disodium dioxido(dioxo)chromium |

| sodium hydroxide | lead dioxide | NaCrO2 | water | sodium chromate | Na2PbO2 molar mass | 39.997 g/mol | 239.2 g/mol | 106.98 g/mol | 18.015 g/mol | 161.97 g/mol | 285.2 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 323 °C | 290 °C | | 0 °C | 780 °C | boiling point | 1390 °C | | | 99.9839 °C | | density | 2.13 g/cm^3 | 9.58 g/cm^3 | | 1 g/cm^3 | 2.698 g/cm^3 | solubility in water | soluble | insoluble | | | | surface tension | 0.07435 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | |