MnSO4 + BaCl2 = MnCl2 + BaSO4

MnSO_4 manganese(II) sulfate + BaCl_2 barium chloride ⟶ MnCl_2 manganese(II) chloride + BaSO_4 barium sulfate

Balance the chemical equation algebraically: MnSO_4 + BaCl_2 ⟶ MnCl_2 + BaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnSO_4 + c_2 BaCl_2 ⟶ c_3 MnCl_2 + c_4 BaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, S, Ba and Cl: Mn: | c_1 = c_3 O: | 4 c_1 = 4 c_4 S: | c_1 = c_4 Ba: | c_2 = c_4 Cl: | 2 c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnSO_4 + BaCl_2 ⟶ MnCl_2 + BaSO_4

+ ⟶ +

manganese(II) sulfate + barium chloride ⟶ manganese(II) chloride + barium sulfate

Construct the equilibrium constant, K, expression for: MnSO_4 + BaCl_2 ⟶ MnCl_2 + BaSO_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: MnSO_4 + BaCl_2 ⟶ MnCl_2 + BaSO_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 MnSO_4 | 1 | -1 BaCl_2 | 1 | -1 MnCl_2 | 1 | 1 BaSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnSO_4 | 1 | -1 | ([MnSO4])^(-1) BaCl_2 | 1 | -1 | ([BaCl2])^(-1) MnCl_2 | 1 | 1 | [MnCl2] BaSO_4 | 1 | 1 | [BaSO4] 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 = ([MnSO4])^(-1) ([BaCl2])^(-1) [MnCl2] [BaSO4] = ([MnCl2] [BaSO4])/([MnSO4] [BaCl2])

Construct the rate of reaction expression for: MnSO_4 + BaCl_2 ⟶ MnCl_2 + BaSO_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: MnSO_4 + BaCl_2 ⟶ MnCl_2 + BaSO_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 MnSO_4 | 1 | -1 BaCl_2 | 1 | -1 MnCl_2 | 1 | 1 BaSO_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 MnSO_4 | 1 | -1 | -(Δ[MnSO4])/(Δt) BaCl_2 | 1 | -1 | -(Δ[BaCl2])/(Δt) MnCl_2 | 1 | 1 | (Δ[MnCl2])/(Δt) BaSO_4 | 1 | 1 | (Δ[BaSO4])/(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[MnSO4])/(Δt) = -(Δ[BaCl2])/(Δt) = (Δ[MnCl2])/(Δt) = (Δ[BaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese(II) sulfate | barium chloride | manganese(II) chloride | barium sulfate formula | MnSO_4 | BaCl_2 | MnCl_2 | BaSO_4 Hill formula | MnSO_4 | BaCl_2 | Cl_2Mn | BaO_4S name | manganese(II) sulfate | barium chloride | manganese(II) chloride | barium sulfate IUPAC name | manganese(+2) cation sulfate | barium(+2) cation dichloride | dichloromanganese | barium(+2) cation sulfate

| manganese(II) sulfate | barium chloride | manganese(II) chloride | barium sulfate molar mass | 150.99 g/mol | 208.2 g/mol | 125.8 g/mol | 233.38 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 710 °C | 963 °C | 652 °C | 1345 °C density | 3.25 g/cm^3 | 3.856 g/cm^3 | 2.98 g/cm^3 | 4.5 g/cm^3 solubility in water | soluble | | | insoluble odor | | odorless | |