Mg + CuO = Cu + MgO

Mg magnesium + CuO cupric oxide ⟶ Cu copper + MgO magnesium oxide

Balance the chemical equation algebraically: Mg + CuO ⟶ Cu + MgO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 CuO ⟶ c_3 Cu + c_4 MgO Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Cu and O: Mg: | 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: | | Mg + CuO ⟶ Cu + MgO

+ ⟶ +

magnesium + cupric oxide ⟶ copper + magnesium oxide

| magnesium | cupric oxide | copper | magnesium oxide molecular enthalpy | 0 kJ/mol | -157.3 kJ/mol | 0 kJ/mol | -601.6 kJ/mol total enthalpy | 0 kJ/mol | -157.3 kJ/mol | 0 kJ/mol | -601.6 kJ/mol | H_initial = -157.3 kJ/mol | | H_final = -601.6 kJ/mol | ΔH_rxn^0 | -601.6 kJ/mol - -157.3 kJ/mol = -444.3 kJ/mol (exothermic) | | |

| magnesium | cupric oxide | copper | magnesium oxide molecular entropy | 33 J/(mol K) | 43 J/(mol K) | 33 J/(mol K) | 27 J/(mol K) total entropy | 33 J/(mol K) | 43 J/(mol K) | 33 J/(mol K) | 27 J/(mol K) | S_initial = 76 J/(mol K) | | S_final = 60 J/(mol K) | ΔS_rxn^0 | 60 J/(mol K) - 76 J/(mol K) = -16 J/(mol K) (exoentropic) | | |

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

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

| magnesium | cupric oxide | copper | magnesium oxide formula | Mg | CuO | Cu | MgO name | magnesium | cupric oxide | copper | magnesium oxide IUPAC name | magnesium | | copper | oxomagnesium

| magnesium | cupric oxide | copper | magnesium oxide molar mass | 24.305 g/mol | 79.545 g/mol | 63.546 g/mol | 40.304 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 1326 °C | 1083 °C | 2852 °C boiling point | 1090 °C | 2000 °C | 2567 °C | 3600 °C density | 1.738 g/cm^3 | 6.315 g/cm^3 | 8.96 g/cm^3 | 3.58 g/cm^3 solubility in water | reacts | insoluble | insoluble | odor | | | odorless | odorless