K2CrO4 + BaCl2 = KCl + BaCrO4

K_2CrO_4 (potassium chromate) + BaCl_2 (barium chloride) ⟶ KCl (potassium chloride) + BaCrO_4 (barium chromate)

Balance the chemical equation algebraically: K_2CrO_4 + BaCl_2 ⟶ KCl + BaCrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2CrO_4 + c_2 BaCl_2 ⟶ c_3 KCl + c_4 BaCrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, K, O, Ba and Cl: Cr: | c_1 = c_4 K: | 2 c_1 = c_3 O: | 4 c_1 = 4 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_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: | | K_2CrO_4 + BaCl_2 ⟶ 2 KCl + BaCrO_4

+ ⟶ +

potassium chromate + barium chloride ⟶ potassium chloride + barium chromate

Construct the equilibrium constant, K, expression for: K_2CrO_4 + BaCl_2 ⟶ KCl + BaCrO_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: K_2CrO_4 + BaCl_2 ⟶ 2 KCl + BaCrO_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 K_2CrO_4 | 1 | -1 BaCl_2 | 1 | -1 KCl | 2 | 2 BaCrO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2CrO_4 | 1 | -1 | ([K2CrO4])^(-1) BaCl_2 | 1 | -1 | ([BaCl2])^(-1) KCl | 2 | 2 | ([KCl])^2 BaCrO_4 | 1 | 1 | [BaCrO4] 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 = ([K2CrO4])^(-1) ([BaCl2])^(-1) ([KCl])^2 [BaCrO4] = (([KCl])^2 [BaCrO4])/([K2CrO4] [BaCl2])

Construct the rate of reaction expression for: K_2CrO_4 + BaCl_2 ⟶ KCl + BaCrO_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: K_2CrO_4 + BaCl_2 ⟶ 2 KCl + BaCrO_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 K_2CrO_4 | 1 | -1 BaCl_2 | 1 | -1 KCl | 2 | 2 BaCrO_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 K_2CrO_4 | 1 | -1 | -(Δ[K2CrO4])/(Δt) BaCl_2 | 1 | -1 | -(Δ[BaCl2])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) BaCrO_4 | 1 | 1 | (Δ[BaCrO4])/(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[K2CrO4])/(Δt) = -(Δ[BaCl2])/(Δt) = 1/2 (Δ[KCl])/(Δt) = (Δ[BaCrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium chromate | barium chloride | potassium chloride | barium chromate formula | K_2CrO_4 | BaCl_2 | KCl | BaCrO_4 Hill formula | CrK_2O_4 | BaCl_2 | ClK | BaCrO_4 name | potassium chromate | barium chloride | potassium chloride | barium chromate IUPAC name | dipotassium dioxido-dioxochromium | barium(+2) cation dichloride | potassium chloride | barium(+2) cation; dioxido-dioxochromium

| potassium chromate | barium chloride | potassium chloride | barium chromate molar mass | 194.19 g/mol | 208.2 g/mol | 74.55 g/mol | 253.32 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 971 °C | 963 °C | 770 °C | 210 °C boiling point | | | 1420 °C | density | 2.73 g/cm^3 | 3.856 g/cm^3 | 1.98 g/cm^3 | 4.5 g/cm^3 solubility in water | soluble | | soluble | odor | odorless | odorless | odorless |