MgCl2 + K2SO3 = KCl + MgSO3

MgCl_2 magnesium chloride + K_2SO_3 potassium sulfite ⟶ KCl potassium chloride + MgSO3

Balance the chemical equation algebraically: MgCl_2 + K_2SO_3 ⟶ KCl + MgSO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgCl_2 + c_2 K_2SO_3 ⟶ c_3 KCl + c_4 MgSO3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Mg, K, O and S: Cl: | 2 c_1 = c_3 Mg: | c_1 = c_4 K: | 2 c_2 = c_3 O: | 3 c_2 = 3 c_4 S: | 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: | | MgCl_2 + K_2SO_3 ⟶ 2 KCl + MgSO3

+ ⟶ + MgSO3

magnesium chloride + potassium sulfite ⟶ potassium chloride + MgSO3

Construct the equilibrium constant, K, expression for: MgCl_2 + K_2SO_3 ⟶ KCl + MgSO3 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: MgCl_2 + K_2SO_3 ⟶ 2 KCl + MgSO3 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 MgCl_2 | 1 | -1 K_2SO_3 | 1 | -1 KCl | 2 | 2 MgSO3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MgCl_2 | 1 | -1 | ([MgCl2])^(-1) K_2SO_3 | 1 | -1 | ([K2SO3])^(-1) KCl | 2 | 2 | ([KCl])^2 MgSO3 | 1 | 1 | [MgSO3] 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 = ([MgCl2])^(-1) ([K2SO3])^(-1) ([KCl])^2 [MgSO3] = (([KCl])^2 [MgSO3])/([MgCl2] [K2SO3])

Construct the rate of reaction expression for: MgCl_2 + K_2SO_3 ⟶ KCl + MgSO3 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: MgCl_2 + K_2SO_3 ⟶ 2 KCl + MgSO3 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 MgCl_2 | 1 | -1 K_2SO_3 | 1 | -1 KCl | 2 | 2 MgSO3 | 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 MgCl_2 | 1 | -1 | -(Δ[MgCl2])/(Δt) K_2SO_3 | 1 | -1 | -(Δ[K2SO3])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) MgSO3 | 1 | 1 | (Δ[MgSO3])/(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[MgCl2])/(Δt) = -(Δ[K2SO3])/(Δt) = 1/2 (Δ[KCl])/(Δt) = (Δ[MgSO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium chloride | potassium sulfite | potassium chloride | MgSO3 formula | MgCl_2 | K_2SO_3 | KCl | MgSO3 Hill formula | Cl_2Mg | K_2O_3S | ClK | MgO3S name | magnesium chloride | potassium sulfite | potassium chloride | IUPAC name | magnesium dichloride | dipotassium sulfite | potassium chloride |

| magnesium chloride | potassium sulfite | potassium chloride | MgSO3 molar mass | 95.2 g/mol | 158.25 g/mol | 74.55 g/mol | 104.4 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 714 °C | | 770 °C | boiling point | | | 1420 °C | density | 2.32 g/cm^3 | | 1.98 g/cm^3 | solubility in water | soluble | | soluble | odor | | | odorless |