Al + CuO = Cu + AlO

Al aluminum + CuO cupric oxide ⟶ Cu copper + AlO

Balance the chemical equation algebraically: Al + CuO ⟶ Cu + AlO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 CuO ⟶ c_3 Cu + c_4 AlO Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Cu and O: Al: | c_1 = c_4 Cu: | c_2 = c_3 O: | c_2 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al + CuO ⟶ Cu + AlO

+ ⟶ + AlO

aluminum + cupric oxide ⟶ copper + AlO

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

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

| aluminum | cupric oxide | copper | AlO formula | Al | CuO | Cu | AlO name | aluminum | cupric oxide | copper |

| aluminum | cupric oxide | copper | AlO molar mass | 26.9815385 g/mol | 79.545 g/mol | 63.546 g/mol | 42.981 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 660.4 °C | 1326 °C | 1083 °C | boiling point | 2460 °C | 2000 °C | 2567 °C | density | 2.7 g/cm^3 | 6.315 g/cm^3 | 8.96 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) | | | odor | odorless | | odorless |