Na2SO4 + CuCl2 = NaCl + CuSO4

Na_2SO_4 sodium sulfate + CuCl_2 copper(II) chloride ⟶ NaCl sodium chloride + CuSO_4 copper(II) sulfate

Balance the chemical equation algebraically: Na_2SO_4 + CuCl_2 ⟶ NaCl + CuSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2SO_4 + c_2 CuCl_2 ⟶ c_3 NaCl + c_4 CuSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, O, S, Cl and Cu: Na: | 2 c_1 = c_3 O: | 4 c_1 = 4 c_4 S: | c_1 = c_4 Cl: | 2 c_2 = c_3 Cu: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Na_2SO_4 + CuCl_2 ⟶ 2 NaCl + CuSO_4

+ ⟶ +

sodium sulfate + copper(II) chloride ⟶ sodium chloride + copper(II) sulfate

| sodium sulfate | copper(II) chloride | sodium chloride | copper(II) sulfate molecular enthalpy | -1387 kJ/mol | -220.1 kJ/mol | -411.2 kJ/mol | -771.4 kJ/mol total enthalpy | -1387 kJ/mol | -220.1 kJ/mol | -822.4 kJ/mol | -771.4 kJ/mol | H_initial = -1607 kJ/mol | | H_final = -1594 kJ/mol | ΔH_rxn^0 | -1594 kJ/mol - -1607 kJ/mol = 13.4 kJ/mol (endothermic) | | |

| sodium sulfate | copper(II) chloride | sodium chloride | copper(II) sulfate molecular free energy | -1270 kJ/mol | -175.7 kJ/mol | -384.1 kJ/mol | -662.2 kJ/mol total free energy | -1270 kJ/mol | -175.7 kJ/mol | -768.2 kJ/mol | -662.2 kJ/mol | G_initial = -1446 kJ/mol | | G_final = -1430 kJ/mol | ΔG_rxn^0 | -1430 kJ/mol - -1446 kJ/mol = 15.5 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: Na_2SO_4 + CuCl_2 ⟶ NaCl + CuSO_4 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: Na_2SO_4 + CuCl_2 ⟶ 2 NaCl + CuSO_4 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 Na_2SO_4 | 1 | -1 CuCl_2 | 1 | -1 NaCl | 2 | 2 CuSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2SO_4 | 1 | -1 | ([Na2SO4])^(-1) CuCl_2 | 1 | -1 | ([CuCl2])^(-1) NaCl | 2 | 2 | ([NaCl])^2 CuSO_4 | 1 | 1 | [CuSO4] 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 = ([Na2SO4])^(-1) ([CuCl2])^(-1) ([NaCl])^2 [CuSO4] = (([NaCl])^2 [CuSO4])/([Na2SO4] [CuCl2])

Construct the rate of reaction expression for: Na_2SO_4 + CuCl_2 ⟶ NaCl + CuSO_4 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: Na_2SO_4 + CuCl_2 ⟶ 2 NaCl + CuSO_4 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 Na_2SO_4 | 1 | -1 CuCl_2 | 1 | -1 NaCl | 2 | 2 CuSO_4 | 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 Na_2SO_4 | 1 | -1 | -(Δ[Na2SO4])/(Δt) CuCl_2 | 1 | -1 | -(Δ[CuCl2])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) CuSO_4 | 1 | 1 | (Δ[CuSO4])/(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[Na2SO4])/(Δt) = -(Δ[CuCl2])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = (Δ[CuSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium sulfate | copper(II) chloride | sodium chloride | copper(II) sulfate formula | Na_2SO_4 | CuCl_2 | NaCl | CuSO_4 Hill formula | Na_2O_4S | Cl_2Cu | ClNa | CuO_4S name | sodium sulfate | copper(II) chloride | sodium chloride | copper(II) sulfate IUPAC name | disodium sulfate | dichlorocopper | sodium chloride | copper sulfate

| sodium sulfate | copper(II) chloride | sodium chloride | copper(II) sulfate molar mass | 142.04 g/mol | 134.4 g/mol | 58.44 g/mol | 159.6 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 884 °C | 620 °C | 801 °C | 200 °C boiling point | 1429 °C | | 1413 °C | density | 2.68 g/cm^3 | 3.386 g/cm^3 | 2.16 g/cm^3 | 3.603 g/cm^3 solubility in water | soluble | | soluble | odor | | | odorless |