Cl2 + KOH = H2O + KCl + KClO2

Cl_2 chlorine + KOH potassium hydroxide ⟶ H_2O water + KCl potassium chloride + KClO2

Balance the chemical equation algebraically: Cl_2 + KOH ⟶ H_2O + KCl + KClO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 KOH ⟶ c_3 H_2O + c_4 KCl + c_5 KClO2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K and O: Cl: | 2 c_1 = c_4 + c_5 H: | c_2 = 2 c_3 K: | c_2 = c_4 + c_5 O: | c_2 = c_3 + 2 c_5 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 4 c_3 = 2 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cl_2 + 4 KOH ⟶ 2 H_2O + 3 KCl + KClO2

+ ⟶ + + KClO2

chlorine + potassium hydroxide ⟶ water + potassium chloride + KClO2

Construct the equilibrium constant, K, expression for: Cl_2 + KOH ⟶ H_2O + KCl + KClO2 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 Cl_2 + 4 KOH ⟶ 2 H_2O + 3 KCl + KClO2 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 | 2 | -2 KOH | 4 | -4 H_2O | 2 | 2 KCl | 3 | 3 KClO2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 2 | -2 | ([Cl2])^(-2) KOH | 4 | -4 | ([KOH])^(-4) H_2O | 2 | 2 | ([H2O])^2 KCl | 3 | 3 | ([KCl])^3 KClO2 | 1 | 1 | [KClO2] 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])^(-2) ([KOH])^(-4) ([H2O])^2 ([KCl])^3 [KClO2] = (([H2O])^2 ([KCl])^3 [KClO2])/(([Cl2])^2 ([KOH])^4)

Construct the rate of reaction expression for: Cl_2 + KOH ⟶ H_2O + KCl + KClO2 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 Cl_2 + 4 KOH ⟶ 2 H_2O + 3 KCl + KClO2 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 | 2 | -2 KOH | 4 | -4 H_2O | 2 | 2 KCl | 3 | 3 KClO2 | 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 Cl_2 | 2 | -2 | -1/2 (Δ[Cl2])/(Δt) KOH | 4 | -4 | -1/4 (Δ[KOH])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(Δt) KClO2 | 1 | 1 | (Δ[KClO2])/(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[Cl2])/(Δt) = -1/4 (Δ[KOH])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/3 (Δ[KCl])/(Δt) = (Δ[KClO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | potassium hydroxide | water | potassium chloride | KClO2 formula | Cl_2 | KOH | H_2O | KCl | KClO2 Hill formula | Cl_2 | HKO | H_2O | ClK | ClKO2 name | chlorine | potassium hydroxide | water | potassium chloride | IUPAC name | molecular chlorine | potassium hydroxide | water | potassium chloride |

| chlorine | potassium hydroxide | water | potassium chloride | KClO2 molar mass | 70.9 g/mol | 56.105 g/mol | 18.015 g/mol | 74.55 g/mol | 106.5 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | melting point | -101 °C | 406 °C | 0 °C | 770 °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 | 1 g/cm^3 | 1.98 g/cm^3 | solubility in water | | 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 |