NaOH + KClO3 + CrCl3 = H2O + NaCl + KCl + Na2CrO4

NaOH sodium hydroxide + KClO_3 potassium chlorate + CrCl_3 chromic chloride ⟶ H_2O water + NaCl sodium chloride + KCl potassium chloride + Na_2CrO_4 sodium chromate

Balance the chemical equation algebraically: NaOH + KClO_3 + CrCl_3 ⟶ H_2O + NaCl + KCl + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KClO_3 + c_3 CrCl_3 ⟶ c_4 H_2O + c_5 NaCl + c_6 KCl + c_7 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Cl, K and Cr: H: | c_1 = 2 c_4 Na: | c_1 = c_5 + 2 c_7 O: | c_1 + 3 c_2 = c_4 + 4 c_7 Cl: | c_2 + 3 c_3 = c_5 + c_6 K: | c_2 = c_6 Cr: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 1 c_3 = 2 c_4 = 5 c_5 = 6 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 NaOH + KClO_3 + 2 CrCl_3 ⟶ 5 H_2O + 6 NaCl + KCl + 2 Na_2CrO_4

+ + ⟶ + + +

sodium hydroxide + potassium chlorate + chromic chloride ⟶ water + sodium chloride + potassium chloride + sodium chromate

Construct the equilibrium constant, K, expression for: NaOH + KClO_3 + CrCl_3 ⟶ H_2O + NaCl + KCl + Na_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: 10 NaOH + KClO_3 + 2 CrCl_3 ⟶ 5 H_2O + 6 NaCl + KCl + 2 Na_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 NaOH | 10 | -10 KClO_3 | 1 | -1 CrCl_3 | 2 | -2 H_2O | 5 | 5 NaCl | 6 | 6 KCl | 1 | 1 Na_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 NaOH | 10 | -10 | ([NaOH])^(-10) KClO_3 | 1 | -1 | ([KClO3])^(-1) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) H_2O | 5 | 5 | ([H2O])^5 NaCl | 6 | 6 | ([NaCl])^6 KCl | 1 | 1 | [KCl] Na_2CrO_4 | 2 | 2 | ([Na2CrO4])^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 = ([NaOH])^(-10) ([KClO3])^(-1) ([CrCl3])^(-2) ([H2O])^5 ([NaCl])^6 [KCl] ([Na2CrO4])^2 = (([H2O])^5 ([NaCl])^6 [KCl] ([Na2CrO4])^2)/(([NaOH])^10 [KClO3] ([CrCl3])^2)

Construct the rate of reaction expression for: NaOH + KClO_3 + CrCl_3 ⟶ H_2O + NaCl + KCl + Na_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: 10 NaOH + KClO_3 + 2 CrCl_3 ⟶ 5 H_2O + 6 NaCl + KCl + 2 Na_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 NaOH | 10 | -10 KClO_3 | 1 | -1 CrCl_3 | 2 | -2 H_2O | 5 | 5 NaCl | 6 | 6 KCl | 1 | 1 Na_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 NaOH | 10 | -10 | -1/10 (Δ[NaOH])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) Na_2CrO_4 | 2 | 2 | 1/2 (Δ[Na2CrO4])/(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 = -1/10 (Δ[NaOH])/(Δt) = -(Δ[KClO3])/(Δt) = -1/2 (Δ[CrCl3])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/6 (Δ[NaCl])/(Δt) = (Δ[KCl])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | potassium chlorate | chromic chloride | water | sodium chloride | potassium chloride | sodium chromate formula | NaOH | KClO_3 | CrCl_3 | H_2O | NaCl | KCl | Na_2CrO_4 Hill formula | HNaO | ClKO_3 | Cl_3Cr | H_2O | ClNa | ClK | CrNa_2O_4 name | sodium hydroxide | potassium chlorate | chromic chloride | water | sodium chloride | potassium chloride | sodium chromate IUPAC name | sodium hydroxide | potassium chlorate | trichlorochromium | water | sodium chloride | potassium chloride | disodium dioxido(dioxo)chromium