Cu + MgCl2 = Mg + CuCl2

Cu copper + MgCl_2 magnesium chloride ⟶ Mg magnesium + CuCl_2 copper(II) chloride

Balance the chemical equation algebraically: Cu + MgCl_2 ⟶ Mg + CuCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 MgCl_2 ⟶ c_3 Mg + c_4 CuCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Cl and Mg: Cu: | c_1 = c_4 Cl: | 2 c_2 = 2 c_4 Mg: | 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_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: | | Cu + MgCl_2 ⟶ Mg + CuCl_2

+ ⟶ +

copper + magnesium chloride ⟶ magnesium + copper(II) chloride

| copper | magnesium chloride | magnesium | copper(II) chloride molecular enthalpy | 0 kJ/mol | -641.3 kJ/mol | 0 kJ/mol | -220.1 kJ/mol total enthalpy | 0 kJ/mol | -641.3 kJ/mol | 0 kJ/mol | -220.1 kJ/mol | H_initial = -641.3 kJ/mol | | H_final = -220.1 kJ/mol | ΔH_rxn^0 | -220.1 kJ/mol - -641.3 kJ/mol = 421.2 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: Cu + MgCl_2 ⟶ Mg + CuCl_2 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: Cu + MgCl_2 ⟶ Mg + CuCl_2 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 Cu | 1 | -1 MgCl_2 | 1 | -1 Mg | 1 | 1 CuCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 1 | -1 | ([Cu])^(-1) MgCl_2 | 1 | -1 | ([MgCl2])^(-1) Mg | 1 | 1 | [Mg] CuCl_2 | 1 | 1 | [CuCl2] 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 = ([Cu])^(-1) ([MgCl2])^(-1) [Mg] [CuCl2] = ([Mg] [CuCl2])/([Cu] [MgCl2])

Construct the rate of reaction expression for: Cu + MgCl_2 ⟶ Mg + CuCl_2 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: Cu + MgCl_2 ⟶ Mg + CuCl_2 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 Cu | 1 | -1 MgCl_2 | 1 | -1 Mg | 1 | 1 CuCl_2 | 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 Cu | 1 | -1 | -(Δ[Cu])/(Δt) MgCl_2 | 1 | -1 | -(Δ[MgCl2])/(Δt) Mg | 1 | 1 | (Δ[Mg])/(Δt) CuCl_2 | 1 | 1 | (Δ[CuCl2])/(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[Cu])/(Δt) = -(Δ[MgCl2])/(Δt) = (Δ[Mg])/(Δt) = (Δ[CuCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper | magnesium chloride | magnesium | copper(II) chloride formula | Cu | MgCl_2 | Mg | CuCl_2 Hill formula | Cu | Cl_2Mg | Mg | Cl_2Cu name | copper | magnesium chloride | magnesium | copper(II) chloride IUPAC name | copper | magnesium dichloride | magnesium | dichlorocopper

| copper | magnesium chloride | magnesium | copper(II) chloride molar mass | 63.546 g/mol | 95.2 g/mol | 24.305 g/mol | 134.4 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1083 °C | 714 °C | 648 °C | 620 °C boiling point | 2567 °C | | 1090 °C | density | 8.96 g/cm^3 | 2.32 g/cm^3 | 1.738 g/cm^3 | 3.386 g/cm^3 solubility in water | insoluble | soluble | reacts | odor | odorless | | |