Al + PbO = Pb + Al2O

Al aluminum + PbO lead monoxide ⟶ Pb lead + Al2O

Balance the chemical equation algebraically: Al + PbO ⟶ Pb + Al2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 PbO ⟶ c_3 Pb + c_4 Al2O Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O and Pb: Al: | c_1 = 2 c_4 O: | c_2 = c_4 Pb: | c_2 = c_3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + PbO ⟶ Pb + Al2O

+ ⟶ + Al2O

aluminum + lead monoxide ⟶ lead + Al2O

Construct the equilibrium constant, K, expression for: Al + PbO ⟶ Pb + Al2O 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 Al + PbO ⟶ Pb + Al2O 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 Al | 2 | -2 PbO | 1 | -1 Pb | 1 | 1 Al2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 2 | -2 | ([Al])^(-2) PbO | 1 | -1 | ([PbO])^(-1) Pb | 1 | 1 | [Pb] Al2O | 1 | 1 | [Al2O] 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 = ([Al])^(-2) ([PbO])^(-1) [Pb] [Al2O] = ([Pb] [Al2O])/(([Al])^2 [PbO])

Construct the rate of reaction expression for: Al + PbO ⟶ Pb + Al2O 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 Al + PbO ⟶ Pb + Al2O 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 Al | 2 | -2 PbO | 1 | -1 Pb | 1 | 1 Al2O | 1 | 1 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 Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) PbO | 1 | -1 | -(Δ[PbO])/(Δt) Pb | 1 | 1 | (Δ[Pb])/(Δt) Al2O | 1 | 1 | (Δ[Al2O])/(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[Al])/(Δt) = -(Δ[PbO])/(Δt) = (Δ[Pb])/(Δt) = (Δ[Al2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | lead monoxide | lead | Al2O formula | Al | PbO | Pb | Al2O Hill formula | Al | OPb | Pb | Al2O name | aluminum | lead monoxide | lead |

| aluminum | lead monoxide | lead | Al2O molar mass | 26.9815385 g/mol | 223.2 g/mol | 207.2 g/mol | 69.962 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 660.4 °C | 886 °C | 327.4 °C | boiling point | 2460 °C | 1470 °C | 1740 °C | density | 2.7 g/cm^3 | 9.5 g/cm^3 | 11.34 g/cm^3 | solubility in water | insoluble | insoluble | insoluble | surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | 1.45×10^-4 Pa s (at 1000 °C) | 0.00183 Pa s (at 38 °C) | odor | odorless | | |