NaCl + MgSO4 = Na2SO4 + MgCl2

NaCl sodium chloride + MgSO_4 magnesium sulfate ⟶ Na_2SO_4 sodium sulfate + MgCl_2 magnesium chloride

Balance the chemical equation algebraically: NaCl + MgSO_4 ⟶ Na_2SO_4 + MgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaCl + c_2 MgSO_4 ⟶ c_3 Na_2SO_4 + c_4 MgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Na, Mg, O and S: Cl: | c_1 = 2 c_4 Na: | c_1 = 2 c_3 Mg: | c_2 = c_4 O: | 4 c_2 = 4 c_3 S: | 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaCl + MgSO_4 ⟶ Na_2SO_4 + MgCl_2

+ ⟶ +

sodium chloride + magnesium sulfate ⟶ sodium sulfate + magnesium chloride

| sodium chloride | magnesium sulfate | sodium sulfate | magnesium chloride molecular enthalpy | -411.2 kJ/mol | -1285 kJ/mol | -1387 kJ/mol | -641.3 kJ/mol total enthalpy | -822.4 kJ/mol | -1285 kJ/mol | -1387 kJ/mol | -641.3 kJ/mol | H_initial = -2107 kJ/mol | | H_final = -2028 kJ/mol | ΔH_rxn^0 | -2028 kJ/mol - -2107 kJ/mol = 78.9 kJ/mol (endothermic) | | |

| sodium chloride | magnesium sulfate | sodium sulfate | magnesium chloride molecular free energy | -384.1 kJ/mol | -1171 kJ/mol | -1270 kJ/mol | -591.8 kJ/mol total free energy | -768.2 kJ/mol | -1171 kJ/mol | -1270 kJ/mol | -591.8 kJ/mol | G_initial = -1939 kJ/mol | | G_final = -1862 kJ/mol | ΔG_rxn^0 | -1862 kJ/mol - -1939 kJ/mol = 76.8 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: NaCl + MgSO_4 ⟶ Na_2SO_4 + 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 + MgSO_4 ⟶ Na_2SO_4 + 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 MgSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 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) MgSO_4 | 1 | -1 | ([MgSO4])^(-1) Na_2SO_4 | 1 | 1 | [Na2SO4] 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) ([MgSO4])^(-1) [Na2SO4] [MgCl2] = ([Na2SO4] [MgCl2])/(([NaCl])^2 [MgSO4])

Construct the rate of reaction expression for: NaCl + MgSO_4 ⟶ Na_2SO_4 + 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 + MgSO_4 ⟶ Na_2SO_4 + 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 MgSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 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) MgSO_4 | 1 | -1 | -(Δ[MgSO4])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(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[MgSO4])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[MgCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium chloride | magnesium sulfate | sodium sulfate | magnesium chloride formula | NaCl | MgSO_4 | Na_2SO_4 | MgCl_2 Hill formula | ClNa | MgO_4S | Na_2O_4S | Cl_2Mg name | sodium chloride | magnesium sulfate | sodium sulfate | magnesium chloride IUPAC name | sodium chloride | magnesium sulfate | disodium sulfate | magnesium dichloride

| sodium chloride | magnesium sulfate | sodium sulfate | magnesium chloride molar mass | 58.44 g/mol | 120.4 g/mol | 142.04 g/mol | 95.2 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 801 °C | | 884 °C | 714 °C boiling point | 1413 °C | | 1429 °C | density | 2.16 g/cm^3 | | 2.68 g/cm^3 | 2.32 g/cm^3 solubility in water | soluble | soluble | soluble | soluble odor | odorless | | |