Cl2 + KOH + CrI3 = H2O + KCl + K2Cr2O7 + KIO4

Cl_2 chlorine + KOH potassium hydroxide + Cr_1I_3 chromium(III) iodide ⟶ H_2O water + KCl potassium chloride + K_2Cr_2O_7 potassium dichromate + KIO_4 potassium periodate

Balance the chemical equation algebraically: Cl_2 + KOH + Cr_1I_3 ⟶ H_2O + KCl + K_2Cr_2O_7 + KIO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 KOH + c_3 Cr_1I_3 ⟶ c_4 H_2O + c_5 KCl + c_6 K_2Cr_2O_7 + c_7 KIO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, O, Cr and I: Cl: | 2 c_1 = c_5 H: | c_2 = 2 c_4 K: | c_2 = c_5 + 2 c_6 + c_7 O: | c_2 = c_4 + 7 c_6 + 4 c_7 Cr: | c_3 = 2 c_6 I: | 3 c_3 = c_7 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 27 c_2 = 62 c_3 = 2 c_4 = 31 c_5 = 54 c_6 = 1 c_7 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 27 Cl_2 + 62 KOH + 2 Cr_1I_3 ⟶ 31 H_2O + 54 KCl + K_2Cr_2O_7 + 6 KIO_4

+ + ⟶ + + +

chlorine + potassium hydroxide + chromium(III) iodide ⟶ water + potassium chloride + potassium dichromate + potassium periodate

Construct the equilibrium constant, K, expression for: Cl_2 + KOH + Cr_1I_3 ⟶ H_2O + KCl + K_2Cr_2O_7 + KIO_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: 27 Cl_2 + 62 KOH + 2 Cr_1I_3 ⟶ 31 H_2O + 54 KCl + K_2Cr_2O_7 + 6 KIO_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 | 27 | -27 KOH | 62 | -62 Cr_1I_3 | 2 | -2 H_2O | 31 | 31 KCl | 54 | 54 K_2Cr_2O_7 | 1 | 1 KIO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 27 | -27 | ([Cl2])^(-27) KOH | 62 | -62 | ([KOH])^(-62) Cr_1I_3 | 2 | -2 | ([Cr1I3])^(-2) H_2O | 31 | 31 | ([H2O])^31 KCl | 54 | 54 | ([KCl])^54 K_2Cr_2O_7 | 1 | 1 | [K2Cr2O7] KIO_4 | 6 | 6 | ([KIO4])^6 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])^(-27) ([KOH])^(-62) ([Cr1I3])^(-2) ([H2O])^31 ([KCl])^54 [K2Cr2O7] ([KIO4])^6 = (([H2O])^31 ([KCl])^54 [K2Cr2O7] ([KIO4])^6)/(([Cl2])^27 ([KOH])^62 ([Cr1I3])^2)

Construct the rate of reaction expression for: Cl_2 + KOH + Cr_1I_3 ⟶ H_2O + KCl + K_2Cr_2O_7 + KIO_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: 27 Cl_2 + 62 KOH + 2 Cr_1I_3 ⟶ 31 H_2O + 54 KCl + K_2Cr_2O_7 + 6 KIO_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 | 27 | -27 KOH | 62 | -62 Cr_1I_3 | 2 | -2 H_2O | 31 | 31 KCl | 54 | 54 K_2Cr_2O_7 | 1 | 1 KIO_4 | 6 | 6 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 | 27 | -27 | -1/27 (Δ[Cl2])/(Δt) KOH | 62 | -62 | -1/62 (Δ[KOH])/(Δt) Cr_1I_3 | 2 | -2 | -1/2 (Δ[Cr1I3])/(Δt) H_2O | 31 | 31 | 1/31 (Δ[H2O])/(Δt) KCl | 54 | 54 | 1/54 (Δ[KCl])/(Δt) K_2Cr_2O_7 | 1 | 1 | (Δ[K2Cr2O7])/(Δt) KIO_4 | 6 | 6 | 1/6 (Δ[KIO4])/(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 = -1/27 (Δ[Cl2])/(Δt) = -1/62 (Δ[KOH])/(Δt) = -1/2 (Δ[Cr1I3])/(Δt) = 1/31 (Δ[H2O])/(Δt) = 1/54 (Δ[KCl])/(Δt) = (Δ[K2Cr2O7])/(Δt) = 1/6 (Δ[KIO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | potassium hydroxide | chromium(III) iodide | water | potassium chloride | potassium dichromate | potassium periodate formula | Cl_2 | KOH | Cr_1I_3 | H_2O | KCl | K_2Cr_2O_7 | KIO_4 Hill formula | Cl_2 | HKO | CrI_3 | H_2O | ClK | Cr_2K_2O_7 | IKO_4 name | chlorine | potassium hydroxide | chromium(III) iodide | water | potassium chloride | potassium dichromate | potassium periodate IUPAC name | molecular chlorine | potassium hydroxide | triiodochromium | water | potassium chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium periodate