AlCl3 + MgSO4 = MgCl2 + Al2(SO4)3

AlCl_3 aluminum chloride + MgSO_4 magnesium sulfate ⟶ MgCl_2 magnesium chloride + Al_2(SO_4)_3 aluminum sulfate

Balance the chemical equation algebraically: AlCl_3 + MgSO_4 ⟶ MgCl_2 + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AlCl_3 + c_2 MgSO_4 ⟶ c_3 MgCl_2 + c_4 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Cl, Mg, O and S: Al: | c_1 = 2 c_4 Cl: | 3 c_1 = 2 c_3 Mg: | c_2 = c_3 O: | 4 c_2 = 12 c_4 S: | c_2 = 3 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 AlCl_3 + 3 MgSO_4 ⟶ 3 MgCl_2 + Al_2(SO_4)_3

+ ⟶ +

aluminum chloride + magnesium sulfate ⟶ magnesium chloride + aluminum sulfate

Construct the equilibrium constant, K, expression for: AlCl_3 + MgSO_4 ⟶ MgCl_2 + Al_2(SO_4)_3 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 AlCl_3 + 3 MgSO_4 ⟶ 3 MgCl_2 + Al_2(SO_4)_3 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 AlCl_3 | 2 | -2 MgSO_4 | 3 | -3 MgCl_2 | 3 | 3 Al_2(SO_4)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AlCl_3 | 2 | -2 | ([AlCl3])^(-2) MgSO_4 | 3 | -3 | ([MgSO4])^(-3) MgCl_2 | 3 | 3 | ([MgCl2])^3 Al_2(SO_4)_3 | 1 | 1 | [Al2(SO4)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 = ([AlCl3])^(-2) ([MgSO4])^(-3) ([MgCl2])^3 [Al2(SO4)3] = (([MgCl2])^3 [Al2(SO4)3])/(([AlCl3])^2 ([MgSO4])^3)

Construct the rate of reaction expression for: AlCl_3 + MgSO_4 ⟶ MgCl_2 + Al_2(SO_4)_3 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 AlCl_3 + 3 MgSO_4 ⟶ 3 MgCl_2 + Al_2(SO_4)_3 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 AlCl_3 | 2 | -2 MgSO_4 | 3 | -3 MgCl_2 | 3 | 3 Al_2(SO_4)_3 | 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 AlCl_3 | 2 | -2 | -1/2 (Δ[AlCl3])/(Δt) MgSO_4 | 3 | -3 | -1/3 (Δ[MgSO4])/(Δt) MgCl_2 | 3 | 3 | 1/3 (Δ[MgCl2])/(Δt) Al_2(SO_4)_3 | 1 | 1 | (Δ[Al2(SO4)3])/(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[AlCl3])/(Δt) = -1/3 (Δ[MgSO4])/(Δt) = 1/3 (Δ[MgCl2])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum chloride | magnesium sulfate | magnesium chloride | aluminum sulfate formula | AlCl_3 | MgSO_4 | MgCl_2 | Al_2(SO_4)_3 Hill formula | AlCl_3 | MgO_4S | Cl_2Mg | Al_2O_12S_3 name | aluminum chloride | magnesium sulfate | magnesium chloride | aluminum sulfate IUPAC name | trichloroalumane | magnesium sulfate | magnesium dichloride | dialuminum trisulfate

| aluminum chloride | magnesium sulfate | magnesium chloride | aluminum sulfate molar mass | 133.3 g/mol | 120.4 g/mol | 95.2 g/mol | 342.1 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 190 °C | | 714 °C | 770 °C density | | | 2.32 g/cm^3 | 2.71 g/cm^3 solubility in water | | soluble | soluble | soluble