BaCl2 + (NH4)2SO4 = NH4Cl + BaSO4

BaCl_2 barium chloride + (NH_4)_2SO_4 ammonium sulfate ⟶ NH_4Cl ammonium chloride + BaSO_4 barium sulfate

Balance the chemical equation algebraically: BaCl_2 + (NH_4)_2SO_4 ⟶ NH_4Cl + BaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 BaCl_2 + c_2 (NH_4)_2SO_4 ⟶ c_3 NH_4Cl + c_4 BaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Ba, Cl, H, N, O and S: Ba: | c_1 = c_4 Cl: | 2 c_1 = c_3 H: | 8 c_2 = 4 c_3 N: | 2 c_2 = c_3 O: | 4 c_2 = 4 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: | | BaCl_2 + (NH_4)_2SO_4 ⟶ 2 NH_4Cl + BaSO_4

+ ⟶ +

barium chloride + ammonium sulfate ⟶ ammonium chloride + barium sulfate

| barium chloride | ammonium sulfate | ammonium chloride | barium sulfate molecular enthalpy | -855 kJ/mol | -1181 kJ/mol | -314.4 kJ/mol | -1473 kJ/mol total enthalpy | -855 kJ/mol | -1181 kJ/mol | -628.8 kJ/mol | -1473 kJ/mol | H_initial = -2036 kJ/mol | | H_final = -2102 kJ/mol | ΔH_rxn^0 | -2102 kJ/mol - -2036 kJ/mol = -66.1 kJ/mol (exothermic) | | |

| barium chloride | ammonium sulfate | ammonium chloride | barium sulfate molecular free energy | -806.7 kJ/mol | -901.7 kJ/mol | -202.9 kJ/mol | -1362 kJ/mol total free energy | -806.7 kJ/mol | -901.7 kJ/mol | -405.8 kJ/mol | -1362 kJ/mol | G_initial = -1708 kJ/mol | | G_final = -1768 kJ/mol | ΔG_rxn^0 | -1768 kJ/mol - -1708 kJ/mol = -59.6 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: BaCl_2 + (NH_4)_2SO_4 ⟶ NH_4Cl + 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: BaCl_2 + (NH_4)_2SO_4 ⟶ 2 NH_4Cl + 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 BaCl_2 | 1 | -1 (NH_4)_2SO_4 | 1 | -1 NH_4Cl | 2 | 2 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 BaCl_2 | 1 | -1 | ([BaCl2])^(-1) (NH_4)_2SO_4 | 1 | -1 | ([(NH4)2SO4])^(-1) NH_4Cl | 2 | 2 | ([NH4Cl])^2 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 = ([BaCl2])^(-1) ([(NH4)2SO4])^(-1) ([NH4Cl])^2 [BaSO4] = (([NH4Cl])^2 [BaSO4])/([BaCl2] [(NH4)2SO4])

Construct the rate of reaction expression for: BaCl_2 + (NH_4)_2SO_4 ⟶ NH_4Cl + 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: BaCl_2 + (NH_4)_2SO_4 ⟶ 2 NH_4Cl + 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 BaCl_2 | 1 | -1 (NH_4)_2SO_4 | 1 | -1 NH_4Cl | 2 | 2 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 BaCl_2 | 1 | -1 | -(Δ[BaCl2])/(Δt) (NH_4)_2SO_4 | 1 | -1 | -(Δ[(NH4)2SO4])/(Δt) NH_4Cl | 2 | 2 | 1/2 (Δ[NH4Cl])/(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[BaCl2])/(Δt) = -(Δ[(NH4)2SO4])/(Δt) = 1/2 (Δ[NH4Cl])/(Δt) = (Δ[BaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| barium chloride | ammonium sulfate | ammonium chloride | barium sulfate formula | BaCl_2 | (NH_4)_2SO_4 | NH_4Cl | BaSO_4 Hill formula | BaCl_2 | H_8N_2O_4S | ClH_4N | BaO_4S name | barium chloride | ammonium sulfate | ammonium chloride | barium sulfate IUPAC name | barium(+2) cation dichloride | | ammonium chloride | barium(+2) cation sulfate

| barium chloride | ammonium sulfate | ammonium chloride | barium sulfate molar mass | 208.2 g/mol | 132.1 g/mol | 53.49 g/mol | 233.38 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 963 °C | 280 °C | 340 °C | 1345 °C density | 3.856 g/cm^3 | 1.77 g/cm^3 | 1.5256 g/cm^3 | 4.5 g/cm^3 solubility in water | | | soluble | insoluble odor | odorless | odorless | |