Fe + MgCl2 = Mg + FeCl2

Fe iron + MgCl_2 magnesium chloride ⟶ Mg magnesium + FeCl_2 iron(II) chloride

Balance the chemical equation algebraically: Fe + MgCl_2 ⟶ Mg + FeCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe + c_2 MgCl_2 ⟶ c_3 Mg + c_4 FeCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, Cl and Mg: Fe: | 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: | | Fe + MgCl_2 ⟶ Mg + FeCl_2

+ ⟶ +

iron + magnesium chloride ⟶ magnesium + iron(II) chloride

| iron | magnesium chloride | magnesium | iron(II) chloride molecular enthalpy | 0 kJ/mol | -641.3 kJ/mol | 0 kJ/mol | -341.8 kJ/mol total enthalpy | 0 kJ/mol | -641.3 kJ/mol | 0 kJ/mol | -341.8 kJ/mol | H_initial = -641.3 kJ/mol | | H_final = -341.8 kJ/mol | ΔH_rxn^0 | -341.8 kJ/mol - -641.3 kJ/mol = 299.5 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: Fe + MgCl_2 ⟶ Mg + FeCl_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: Fe + MgCl_2 ⟶ Mg + FeCl_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 Fe | 1 | -1 MgCl_2 | 1 | -1 Mg | 1 | 1 FeCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe | 1 | -1 | ([Fe])^(-1) MgCl_2 | 1 | -1 | ([MgCl2])^(-1) Mg | 1 | 1 | [Mg] FeCl_2 | 1 | 1 | [FeCl2] 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 = ([Fe])^(-1) ([MgCl2])^(-1) [Mg] [FeCl2] = ([Mg] [FeCl2])/([Fe] [MgCl2])

Construct the rate of reaction expression for: Fe + MgCl_2 ⟶ Mg + FeCl_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: Fe + MgCl_2 ⟶ Mg + FeCl_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 Fe | 1 | -1 MgCl_2 | 1 | -1 Mg | 1 | 1 FeCl_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 Fe | 1 | -1 | -(Δ[Fe])/(Δt) MgCl_2 | 1 | -1 | -(Δ[MgCl2])/(Δt) Mg | 1 | 1 | (Δ[Mg])/(Δt) FeCl_2 | 1 | 1 | (Δ[FeCl2])/(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[Fe])/(Δt) = -(Δ[MgCl2])/(Δt) = (Δ[Mg])/(Δt) = (Δ[FeCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron | magnesium chloride | magnesium | iron(II) chloride formula | Fe | MgCl_2 | Mg | FeCl_2 Hill formula | Fe | Cl_2Mg | Mg | Cl_2Fe name | iron | magnesium chloride | magnesium | iron(II) chloride IUPAC name | iron | magnesium dichloride | magnesium | dichloroiron

| iron | magnesium chloride | magnesium | iron(II) chloride molar mass | 55.845 g/mol | 95.2 g/mol | 24.305 g/mol | 126.7 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1535 °C | 714 °C | 648 °C | 677 °C boiling point | 2750 °C | | 1090 °C | density | 7.874 g/cm^3 | 2.32 g/cm^3 | 1.738 g/cm^3 | 3.16 g/cm^3 solubility in water | insoluble | soluble | reacts |