Cl2 + KOH + CrCl3 = H2O + KCl + K2CrO4

Cl_2 chlorine + KOH potassium hydroxide + CrCl_3 chromic chloride ⟶ H_2O water + KCl potassium chloride + K_2CrO_4 potassium chromate

Balance the chemical equation algebraically: Cl_2 + KOH + CrCl_3 ⟶ H_2O + KCl + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 KOH + c_3 CrCl_3 ⟶ c_4 H_2O + c_5 KCl + c_6 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, O and Cr: Cl: | 2 c_1 + 3 c_3 = c_5 H: | c_2 = 2 c_4 K: | c_2 = c_5 + 2 c_6 O: | c_2 = c_4 + 4 c_6 Cr: | c_3 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 8 c_3 = 1 c_4 = 4 c_5 = 6 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 16 c_3 = 2 c_4 = 8 c_5 = 12 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cl_2 + 16 KOH + 2 CrCl_3 ⟶ 8 H_2O + 12 KCl + 2 K_2CrO_4

+ + ⟶ + +

chlorine + potassium hydroxide + chromic chloride ⟶ water + potassium chloride + potassium chromate

Construct the equilibrium constant, K, expression for: Cl_2 + KOH + CrCl_3 ⟶ H_2O + KCl + K_2CrO_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: 3 Cl_2 + 16 KOH + 2 CrCl_3 ⟶ 8 H_2O + 12 KCl + 2 K_2CrO_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 Cl_2 | 3 | -3 KOH | 16 | -16 CrCl_3 | 2 | -2 H_2O | 8 | 8 KCl | 12 | 12 K_2CrO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 3 | -3 | ([Cl2])^(-3) KOH | 16 | -16 | ([KOH])^(-16) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) H_2O | 8 | 8 | ([H2O])^8 KCl | 12 | 12 | ([KCl])^12 K_2CrO_4 | 2 | 2 | ([K2CrO4])^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 = ([Cl2])^(-3) ([KOH])^(-16) ([CrCl3])^(-2) ([H2O])^8 ([KCl])^12 ([K2CrO4])^2 = (([H2O])^8 ([KCl])^12 ([K2CrO4])^2)/(([Cl2])^3 ([KOH])^16 ([CrCl3])^2)

Construct the rate of reaction expression for: Cl_2 + KOH + CrCl_3 ⟶ H_2O + KCl + K_2CrO_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: 3 Cl_2 + 16 KOH + 2 CrCl_3 ⟶ 8 H_2O + 12 KCl + 2 K_2CrO_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 Cl_2 | 3 | -3 KOH | 16 | -16 CrCl_3 | 2 | -2 H_2O | 8 | 8 KCl | 12 | 12 K_2CrO_4 | 2 | 2 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 Cl_2 | 3 | -3 | -1/3 (Δ[Cl2])/(Δt) KOH | 16 | -16 | -1/16 (Δ[KOH])/(Δt) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) KCl | 12 | 12 | 1/12 (Δ[KCl])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(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 = -1/3 (Δ[Cl2])/(Δt) = -1/16 (Δ[KOH])/(Δt) = -1/2 (Δ[CrCl3])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/12 (Δ[KCl])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | potassium hydroxide | chromic chloride | water | potassium chloride | potassium chromate formula | Cl_2 | KOH | CrCl_3 | H_2O | KCl | K_2CrO_4 Hill formula | Cl_2 | HKO | Cl_3Cr | H_2O | ClK | CrK_2O_4 name | chlorine | potassium hydroxide | chromic chloride | water | potassium chloride | potassium chromate IUPAC name | molecular chlorine | potassium hydroxide | trichlorochromium | water | potassium chloride | dipotassium dioxido-dioxochromium

| chlorine | potassium hydroxide | chromic chloride | water | potassium chloride | potassium chromate molar mass | 70.9 g/mol | 56.105 g/mol | 158.3 g/mol | 18.015 g/mol | 74.55 g/mol | 194.19 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -101 °C | 406 °C | 1152 °C | 0 °C | 770 °C | 971 °C boiling point | -34 °C | 1327 °C | | 99.9839 °C | 1420 °C | density | 0.003214 g/cm^3 (at 0 °C) | 2.044 g/cm^3 | 2.87 g/cm^3 | 1 g/cm^3 | 1.98 g/cm^3 | 2.73 g/cm^3 solubility in water | | soluble | slightly soluble | | soluble | soluble surface tension | | | | 0.0728 N/m | | dynamic viscosity | | 0.001 Pa s (at 550 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | odorless | odorless