Cl2 + Ca(OH)2 = H2O + CaCl2 + Ca(OCl)2

Cl_2 chlorine + Ca(OH)_2 calcium hydroxide ⟶ H_2O water + CaCl_2 calcium chloride + Ca(OCl)2

Balance the chemical equation algebraically: Cl_2 + Ca(OH)_2 ⟶ H_2O + CaCl_2 + Ca(OCl)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 Ca(OH)_2 ⟶ c_3 H_2O + c_4 CaCl_2 + c_5 Ca(OCl)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Ca, H and O: Cl: | 2 c_1 = 2 c_4 + 2 c_5 Ca: | c_2 = c_4 + c_5 H: | 2 c_2 = 2 c_3 O: | 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cl_2 + 2 Ca(OH)_2 ⟶ 2 H_2O + CaCl_2 + Ca(OCl)2

+ ⟶ + + Ca(OCl)2

chlorine + calcium hydroxide ⟶ water + calcium chloride + Ca(OCl)2

Construct the equilibrium constant, K, expression for: Cl_2 + Ca(OH)_2 ⟶ H_2O + CaCl_2 + Ca(OCl)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 Cl_2 + 2 Ca(OH)_2 ⟶ 2 H_2O + CaCl_2 + Ca(OCl)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 Cl_2 | 2 | -2 Ca(OH)_2 | 2 | -2 H_2O | 2 | 2 CaCl_2 | 1 | 1 Ca(OCl)2 | 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) Ca(OH)_2 | 2 | -2 | ([Ca(OH)2])^(-2) H_2O | 2 | 2 | ([H2O])^2 CaCl_2 | 1 | 1 | [CaCl2] Ca(OCl)2 | 1 | 1 | [Ca(OCl)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])^(-2) ([Ca(OH)2])^(-2) ([H2O])^2 [CaCl2] [Ca(OCl)2] = (([H2O])^2 [CaCl2] [Ca(OCl)2])/(([Cl2])^2 ([Ca(OH)2])^2)

Construct the rate of reaction expression for: Cl_2 + Ca(OH)_2 ⟶ H_2O + CaCl_2 + Ca(OCl)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 Cl_2 + 2 Ca(OH)_2 ⟶ 2 H_2O + CaCl_2 + Ca(OCl)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 Cl_2 | 2 | -2 Ca(OH)_2 | 2 | -2 H_2O | 2 | 2 CaCl_2 | 1 | 1 Ca(OCl)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 Cl_2 | 2 | -2 | -1/2 (Δ[Cl2])/(Δt) Ca(OH)_2 | 2 | -2 | -1/2 (Δ[Ca(OH)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CaCl_2 | 1 | 1 | (Δ[CaCl2])/(Δt) Ca(OCl)2 | 1 | 1 | (Δ[Ca(OCl)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[Cl2])/(Δt) = -1/2 (Δ[Ca(OH)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[CaCl2])/(Δt) = (Δ[Ca(OCl)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | calcium hydroxide | water | calcium chloride | Ca(OCl)2 formula | Cl_2 | Ca(OH)_2 | H_2O | CaCl_2 | Ca(OCl)2 Hill formula | Cl_2 | CaH_2O_2 | H_2O | CaCl_2 | CaCl2O2 name | chlorine | calcium hydroxide | water | calcium chloride | IUPAC name | molecular chlorine | calcium dihydroxide | water | calcium dichloride |