HCl + K2Cr2O7 + CH3OH = H2O + KCl + CrCl3 + HCOOH

HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + CH_3OH methanol ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride + HCOOH formic acid

Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + CH_3OH ⟶ H_2O + KCl + CrCl_3 + HCOOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 CH_3OH ⟶ c_4 H_2O + c_5 KCl + c_6 CrCl_3 + c_7 HCOOH Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr, K, O and C: Cl: | c_1 = c_5 + 3 c_6 H: | c_1 + 4 c_3 = 2 c_4 + 2 c_7 Cr: | 2 c_2 = c_6 K: | 2 c_2 = c_5 O: | 7 c_2 + c_3 = c_4 + 2 c_7 C: | 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 = 8 c_2 = 1 c_3 = 3/2 c_4 = 11/2 c_5 = 2 c_6 = 2 c_7 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 2 c_3 = 3 c_4 = 11 c_5 = 4 c_6 = 4 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 HCl + 2 K_2Cr_2O_7 + 3 CH_3OH ⟶ 11 H_2O + 4 KCl + 4 CrCl_3 + 3 HCOOH

+ + ⟶ + + +

hydrogen chloride + potassium dichromate + methanol ⟶ water + potassium chloride + chromic chloride + formic acid

Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + CH_3OH ⟶ H_2O + KCl + CrCl_3 + HCOOH 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: 16 HCl + 2 K_2Cr_2O_7 + 3 CH_3OH ⟶ 11 H_2O + 4 KCl + 4 CrCl_3 + 3 HCOOH 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 HCl | 16 | -16 K_2Cr_2O_7 | 2 | -2 CH_3OH | 3 | -3 H_2O | 11 | 11 KCl | 4 | 4 CrCl_3 | 4 | 4 HCOOH | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 16 | -16 | ([HCl])^(-16) K_2Cr_2O_7 | 2 | -2 | ([K2Cr2O7])^(-2) CH_3OH | 3 | -3 | ([CH3OH])^(-3) H_2O | 11 | 11 | ([H2O])^11 KCl | 4 | 4 | ([KCl])^4 CrCl_3 | 4 | 4 | ([CrCl3])^4 HCOOH | 3 | 3 | ([HCOOH])^3 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 = ([HCl])^(-16) ([K2Cr2O7])^(-2) ([CH3OH])^(-3) ([H2O])^11 ([KCl])^4 ([CrCl3])^4 ([HCOOH])^3 = (([H2O])^11 ([KCl])^4 ([CrCl3])^4 ([HCOOH])^3)/(([HCl])^16 ([K2Cr2O7])^2 ([CH3OH])^3)

Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + CH_3OH ⟶ H_2O + KCl + CrCl_3 + HCOOH 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: 16 HCl + 2 K_2Cr_2O_7 + 3 CH_3OH ⟶ 11 H_2O + 4 KCl + 4 CrCl_3 + 3 HCOOH 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 HCl | 16 | -16 K_2Cr_2O_7 | 2 | -2 CH_3OH | 3 | -3 H_2O | 11 | 11 KCl | 4 | 4 CrCl_3 | 4 | 4 HCOOH | 3 | 3 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 HCl | 16 | -16 | -1/16 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 2 | -2 | -1/2 (Δ[K2Cr2O7])/(Δt) CH_3OH | 3 | -3 | -1/3 (Δ[CH3OH])/(Δt) H_2O | 11 | 11 | 1/11 (Δ[H2O])/(Δt) KCl | 4 | 4 | 1/4 (Δ[KCl])/(Δt) CrCl_3 | 4 | 4 | 1/4 (Δ[CrCl3])/(Δt) HCOOH | 3 | 3 | 1/3 (Δ[HCOOH])/(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 = -1/16 (Δ[HCl])/(Δt) = -1/2 (Δ[K2Cr2O7])/(Δt) = -1/3 (Δ[CH3OH])/(Δt) = 1/11 (Δ[H2O])/(Δt) = 1/4 (Δ[KCl])/(Δt) = 1/4 (Δ[CrCl3])/(Δt) = 1/3 (Δ[HCOOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium dichromate | methanol | water | potassium chloride | chromic chloride | formic acid formula | HCl | K_2Cr_2O_7 | CH_3OH | H_2O | KCl | CrCl_3 | HCOOH Hill formula | ClH | Cr_2K_2O_7 | CH_4O | H_2O | ClK | Cl_3Cr | CH_2O_2 name | hydrogen chloride | potassium dichromate | methanol | water | potassium chloride | chromic chloride | formic acid IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | methanol | water | potassium chloride | trichlorochromium | formic acid