I2 + CrCl3 + Na(OH) = H2O + NaI + Na2CrO4 + NaClO4

I_2 iodine + CrCl_3 chromic chloride + NaOH sodium hydroxide ⟶ H_2O water + NaI sodium iodide + Na_2CrO_4 sodium chromate + NaClO_4 sodium perchlorate

Balance the chemical equation algebraically: I_2 + CrCl_3 + NaOH ⟶ H_2O + NaI + Na_2CrO_4 + NaClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 I_2 + c_2 CrCl_3 + c_3 NaOH ⟶ c_4 H_2O + c_5 NaI + c_6 Na_2CrO_4 + c_7 NaClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for I, Cl, Cr, H, Na and O: I: | 2 c_1 = c_5 Cl: | 3 c_2 = c_7 Cr: | c_2 = c_6 H: | c_3 = 2 c_4 Na: | c_3 = c_5 + 2 c_6 + c_7 O: | c_3 = c_4 + 4 c_6 + 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 27/2 c_2 = 1 c_3 = 32 c_4 = 16 c_5 = 27 c_6 = 1 c_7 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 27 c_2 = 2 c_3 = 64 c_4 = 32 c_5 = 54 c_6 = 2 c_7 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 27 I_2 + 2 CrCl_3 + 64 NaOH ⟶ 32 H_2O + 54 NaI + 2 Na_2CrO_4 + 6 NaClO_4

+ + ⟶ + + +

iodine + chromic chloride + sodium hydroxide ⟶ water + sodium iodide + sodium chromate + sodium perchlorate

Construct the equilibrium constant, K, expression for: I_2 + CrCl_3 + NaOH ⟶ H_2O + NaI + Na_2CrO_4 + NaClO_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 I_2 + 2 CrCl_3 + 64 NaOH ⟶ 32 H_2O + 54 NaI + 2 Na_2CrO_4 + 6 NaClO_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 I_2 | 27 | -27 CrCl_3 | 2 | -2 NaOH | 64 | -64 H_2O | 32 | 32 NaI | 54 | 54 Na_2CrO_4 | 2 | 2 NaClO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression I_2 | 27 | -27 | ([I2])^(-27) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) NaOH | 64 | -64 | ([NaOH])^(-64) H_2O | 32 | 32 | ([H2O])^32 NaI | 54 | 54 | ([NaI])^54 Na_2CrO_4 | 2 | 2 | ([Na2CrO4])^2 NaClO_4 | 6 | 6 | ([NaClO4])^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 = ([I2])^(-27) ([CrCl3])^(-2) ([NaOH])^(-64) ([H2O])^32 ([NaI])^54 ([Na2CrO4])^2 ([NaClO4])^6 = (([H2O])^32 ([NaI])^54 ([Na2CrO4])^2 ([NaClO4])^6)/(([I2])^27 ([CrCl3])^2 ([NaOH])^64)

Construct the rate of reaction expression for: I_2 + CrCl_3 + NaOH ⟶ H_2O + NaI + Na_2CrO_4 + NaClO_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 I_2 + 2 CrCl_3 + 64 NaOH ⟶ 32 H_2O + 54 NaI + 2 Na_2CrO_4 + 6 NaClO_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 I_2 | 27 | -27 CrCl_3 | 2 | -2 NaOH | 64 | -64 H_2O | 32 | 32 NaI | 54 | 54 Na_2CrO_4 | 2 | 2 NaClO_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 I_2 | 27 | -27 | -1/27 (Δ[I2])/(Δt) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) NaOH | 64 | -64 | -1/64 (Δ[NaOH])/(Δt) H_2O | 32 | 32 | 1/32 (Δ[H2O])/(Δt) NaI | 54 | 54 | 1/54 (Δ[NaI])/(Δt) Na_2CrO_4 | 2 | 2 | 1/2 (Δ[Na2CrO4])/(Δt) NaClO_4 | 6 | 6 | 1/6 (Δ[NaClO4])/(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[I2])/(Δt) = -1/2 (Δ[CrCl3])/(Δt) = -1/64 (Δ[NaOH])/(Δt) = 1/32 (Δ[H2O])/(Δt) = 1/54 (Δ[NaI])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) = 1/6 (Δ[NaClO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iodine | chromic chloride | sodium hydroxide | water | sodium iodide | sodium chromate | sodium perchlorate formula | I_2 | CrCl_3 | NaOH | H_2O | NaI | Na_2CrO_4 | NaClO_4 Hill formula | I_2 | Cl_3Cr | HNaO | H_2O | INa | CrNa_2O_4 | ClNaO_4 name | iodine | chromic chloride | sodium hydroxide | water | sodium iodide | sodium chromate | sodium perchlorate IUPAC name | molecular iodine | trichlorochromium | sodium hydroxide | water | sodium iodide | disodium dioxido(dioxo)chromium | sodium perchlorate