NaCl + Mg = Na + MgCl2

NaCl sodium chloride + Mg magnesium ⟶ Na sodium + MgCl_2 magnesium chloride

Balance the chemical equation algebraically: NaCl + Mg ⟶ Na + MgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaCl + c_2 Mg ⟶ c_3 Na + c_4 MgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Na and Mg: Cl: | c_1 = 2 c_4 Na: | c_1 = c_3 Mg: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaCl + Mg ⟶ 2 Na + MgCl_2

+ ⟶ +

sodium chloride + magnesium ⟶ sodium + magnesium chloride

| sodium chloride | magnesium | sodium | magnesium chloride molecular enthalpy | -411.2 kJ/mol | 0 kJ/mol | 0 kJ/mol | -641.3 kJ/mol total enthalpy | -822.4 kJ/mol | 0 kJ/mol | 0 kJ/mol | -641.3 kJ/mol | H_initial = -822.4 kJ/mol | | H_final = -641.3 kJ/mol | ΔH_rxn^0 | -641.3 kJ/mol - -822.4 kJ/mol = 181.1 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: NaCl + Mg ⟶ Na + 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: 2 NaCl + Mg ⟶ 2 Na + 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 NaCl | 2 | -2 Mg | 1 | -1 Na | 2 | 2 MgCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaCl | 2 | -2 | ([NaCl])^(-2) Mg | 1 | -1 | ([Mg])^(-1) Na | 2 | 2 | ([Na])^2 MgCl_2 | 1 | 1 | [MgCl2] 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 = ([NaCl])^(-2) ([Mg])^(-1) ([Na])^2 [MgCl2] = (([Na])^2 [MgCl2])/(([NaCl])^2 [Mg])

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

| sodium chloride | magnesium | sodium | magnesium chloride formula | NaCl | Mg | Na | MgCl_2 Hill formula | ClNa | Mg | Na | Cl_2Mg name | sodium chloride | magnesium | sodium | magnesium chloride IUPAC name | sodium chloride | magnesium | sodium | magnesium dichloride

| sodium chloride | magnesium | sodium | magnesium chloride molar mass | 58.44 g/mol | 24.305 g/mol | 22.98976928 g/mol | 95.2 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 801 °C | 648 °C | 97.8 °C | 714 °C boiling point | 1413 °C | 1090 °C | 883 °C | density | 2.16 g/cm^3 | 1.738 g/cm^3 | 0.968 g/cm^3 | 2.32 g/cm^3 solubility in water | soluble | reacts | decomposes | soluble dynamic viscosity | | | 1.413×10^-5 Pa s (at 527 °C) | odor | odorless | | |