Mg + FeCl3 = Fe + MgCl2

Mg magnesium + FeCl_3 iron(III) chloride ⟶ Fe iron + MgCl_2 magnesium chloride

Balance the chemical equation algebraically: Mg + FeCl_3 ⟶ Fe + MgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 FeCl_3 ⟶ c_3 Fe + c_4 MgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Cl and Fe: Mg: | c_1 = c_4 Cl: | 3 c_2 = 2 c_4 Fe: | 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 = 3/2 c_2 = 1 c_3 = 1 c_4 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Mg + 2 FeCl_3 ⟶ 2 Fe + 3 MgCl_2

+ ⟶ +

magnesium + iron(III) chloride ⟶ iron + magnesium chloride

| magnesium | iron(III) chloride | iron | magnesium chloride molecular enthalpy | 0 kJ/mol | -399.5 kJ/mol | 0 kJ/mol | -641.3 kJ/mol total enthalpy | 0 kJ/mol | -799 kJ/mol | 0 kJ/mol | -1924 kJ/mol | H_initial = -799 kJ/mol | | H_final = -1924 kJ/mol | ΔH_rxn^0 | -1924 kJ/mol - -799 kJ/mol = -1125 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Mg + FeCl_3 ⟶ Fe + MgCl_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: 3 Mg + 2 FeCl_3 ⟶ 2 Fe + 3 MgCl_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 Mg | 3 | -3 FeCl_3 | 2 | -2 Fe | 2 | 2 MgCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 3 | -3 | ([Mg])^(-3) FeCl_3 | 2 | -2 | ([FeCl3])^(-2) Fe | 2 | 2 | ([Fe])^2 MgCl_2 | 3 | 3 | ([MgCl2])^3 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])^(-3) ([FeCl3])^(-2) ([Fe])^2 ([MgCl2])^3 = (([Fe])^2 ([MgCl2])^3)/(([Mg])^3 ([FeCl3])^2)

Construct the rate of reaction expression for: Mg + FeCl_3 ⟶ Fe + MgCl_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: 3 Mg + 2 FeCl_3 ⟶ 2 Fe + 3 MgCl_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 Mg | 3 | -3 FeCl_3 | 2 | -2 Fe | 2 | 2 MgCl_2 | 3 | 3 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 | 3 | -3 | -1/3 (Δ[Mg])/(Δt) FeCl_3 | 2 | -2 | -1/2 (Δ[FeCl3])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) MgCl_2 | 3 | 3 | 1/3 (Δ[MgCl2])/(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 = -1/3 (Δ[Mg])/(Δt) = -1/2 (Δ[FeCl3])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[MgCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | iron(III) chloride | iron | magnesium chloride formula | Mg | FeCl_3 | Fe | MgCl_2 Hill formula | Mg | Cl_3Fe | Fe | Cl_2Mg name | magnesium | iron(III) chloride | iron | magnesium chloride IUPAC name | magnesium | trichloroiron | iron | magnesium dichloride

| magnesium | iron(III) chloride | iron | magnesium chloride molar mass | 24.305 g/mol | 162.2 g/mol | 55.845 g/mol | 95.2 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 304 °C | 1535 °C | 714 °C boiling point | 1090 °C | | 2750 °C | density | 1.738 g/cm^3 | | 7.874 g/cm^3 | 2.32 g/cm^3 solubility in water | reacts | | insoluble | soluble