AgNO3 + BaCl2 = AgCl + Ba(NO3)2

AgNO_3 (silver nitrate) + BaCl_2 (barium chloride) ⟶ AgCl (silver chloride) + Ba(NO_3)_2 (barium nitrate)

Balance the chemical equation algebraically: AgNO_3 + BaCl_2 ⟶ AgCl + Ba(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 BaCl_2 ⟶ c_3 AgCl + c_4 Ba(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O, Ba and Cl: Ag: | c_1 = c_3 N: | c_1 = 2 c_4 O: | 3 c_1 = 6 c_4 Ba: | c_2 = c_4 Cl: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 AgNO_3 + BaCl_2 ⟶ 2 AgCl + Ba(NO_3)_2

+ ⟶ +

silver nitrate + barium chloride ⟶ silver chloride + barium nitrate

| silver nitrate | barium chloride | silver chloride | barium nitrate molecular enthalpy | -124.4 kJ/mol | -855 kJ/mol | -127 kJ/mol | -988 kJ/mol total enthalpy | -248.8 kJ/mol | -855 kJ/mol | -254 kJ/mol | -988 kJ/mol | H_initial = -1104 kJ/mol | | H_final = -1242 kJ/mol | ΔH_rxn^0 | -1242 kJ/mol - -1104 kJ/mol = -138.2 kJ/mol (exothermic) | | |

| silver nitrate | barium chloride | silver chloride | barium nitrate molecular free energy | -33.4 kJ/mol | -806.7 kJ/mol | -109.8 kJ/mol | -7926 kJ/mol total free energy | -66.8 kJ/mol | -806.7 kJ/mol | -219.6 kJ/mol | -7926 kJ/mol | G_initial = -873.5 kJ/mol | | G_final = -8146 kJ/mol | ΔG_rxn^0 | -8146 kJ/mol - -873.5 kJ/mol = -7272 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: AgNO_3 + BaCl_2 ⟶ AgCl + Ba(NO_3)_2 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 AgNO_3 + BaCl_2 ⟶ 2 AgCl + Ba(NO_3)_2 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 AgNO_3 | 2 | -2 BaCl_2 | 1 | -1 AgCl | 2 | 2 Ba(NO_3)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AgNO_3 | 2 | -2 | ([AgNO3])^(-2) BaCl_2 | 1 | -1 | ([BaCl2])^(-1) AgCl | 2 | 2 | ([AgCl])^2 Ba(NO_3)_2 | 1 | 1 | [Ba(NO3)2] 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 = ([AgNO3])^(-2) ([BaCl2])^(-1) ([AgCl])^2 [Ba(NO3)2] = (([AgCl])^2 [Ba(NO3)2])/(([AgNO3])^2 [BaCl2])

Construct the rate of reaction expression for: AgNO_3 + BaCl_2 ⟶ AgCl + Ba(NO_3)_2 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 AgNO_3 + BaCl_2 ⟶ 2 AgCl + Ba(NO_3)_2 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 AgNO_3 | 2 | -2 BaCl_2 | 1 | -1 AgCl | 2 | 2 Ba(NO_3)_2 | 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 AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) BaCl_2 | 1 | -1 | -(Δ[BaCl2])/(Δt) AgCl | 2 | 2 | 1/2 (Δ[AgCl])/(Δt) Ba(NO_3)_2 | 1 | 1 | (Δ[Ba(NO3)2])/(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[AgNO3])/(Δt) = -(Δ[BaCl2])/(Δt) = 1/2 (Δ[AgCl])/(Δt) = (Δ[Ba(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silver nitrate | barium chloride | silver chloride | barium nitrate formula | AgNO_3 | BaCl_2 | AgCl | Ba(NO_3)_2 Hill formula | AgNO_3 | BaCl_2 | AgCl | BaN_2O_6 name | silver nitrate | barium chloride | silver chloride | barium nitrate IUPAC name | silver nitrate | barium(+2) cation dichloride | chlorosilver | barium(+2) cation dinitrate

| silver nitrate | barium chloride | silver chloride | barium nitrate molar mass | 169.87 g/mol | 208.2 g/mol | 143.32 g/mol | 261.34 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 212 °C | 963 °C | 455 °C | 592 °C boiling point | | | 1554 °C | density | | 3.856 g/cm^3 | 5.56 g/cm^3 | 3.23 g/cm^3 solubility in water | soluble | | | odor | odorless | odorless | |