H2SO4 + K2Cr2O7 + C2H5OH = H2O + K2SO4 + Cr2(SO4)3 + C2H4O2

H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + CH_3CH_2OH ethanol ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + CH_3CO_2H acetic acid

Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + CH_3CO_2H Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 + c_3 CH_3CH_2OH ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 CH_3CO_2H Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, K and C: H: | 2 c_1 + 6 c_3 = 2 c_4 + 4 c_7 O: | 4 c_1 + 7 c_2 + c_3 = c_4 + 4 c_5 + 12 c_6 + 2 c_7 S: | c_1 = c_5 + 3 c_6 Cr: | 2 c_2 = 2 c_6 K: | 2 c_2 = 2 c_5 C: | 2 c_3 = 2 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 = 4 c_2 = 1 c_3 = 3/2 c_4 = 11/2 c_5 = 1 c_6 = 1 c_7 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 2 c_3 = 3 c_4 = 11 c_5 = 2 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 2 K_2Cr_2O_7 + 3 CH_3CH_2OH ⟶ 11 H_2O + 2 K_2SO_4 + 2 Cr_2(SO_4)_3 + 3 CH_3CO_2H

+ + ⟶ + + +

sulfuric acid + potassium dichromate + ethanol ⟶ water + potassium sulfate + chromium sulfate + acetic acid

Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + CH_3CO_2H 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: 8 H_2SO_4 + 2 K_2Cr_2O_7 + 3 CH_3CH_2OH ⟶ 11 H_2O + 2 K_2SO_4 + 2 Cr_2(SO_4)_3 + 3 CH_3CO_2H 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 H_2SO_4 | 8 | -8 K_2Cr_2O_7 | 2 | -2 CH_3CH_2OH | 3 | -3 H_2O | 11 | 11 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 2 | 2 CH_3CO_2H | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 8 | -8 | ([H2SO4])^(-8) K_2Cr_2O_7 | 2 | -2 | ([K2Cr2O7])^(-2) CH_3CH_2OH | 3 | -3 | ([CH3CH2OH])^(-3) H_2O | 11 | 11 | ([H2O])^11 K_2SO_4 | 2 | 2 | ([K2SO4])^2 Cr_2(SO_4)_3 | 2 | 2 | ([Cr2(SO4)3])^2 CH_3CO_2H | 3 | 3 | ([CH3CO2H])^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 = ([H2SO4])^(-8) ([K2Cr2O7])^(-2) ([CH3CH2OH])^(-3) ([H2O])^11 ([K2SO4])^2 ([Cr2(SO4)3])^2 ([CH3CO2H])^3 = (([H2O])^11 ([K2SO4])^2 ([Cr2(SO4)3])^2 ([CH3CO2H])^3)/(([H2SO4])^8 ([K2Cr2O7])^2 ([CH3CH2OH])^3)

Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + CH_3CO_2H 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: 8 H_2SO_4 + 2 K_2Cr_2O_7 + 3 CH_3CH_2OH ⟶ 11 H_2O + 2 K_2SO_4 + 2 Cr_2(SO_4)_3 + 3 CH_3CO_2H 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 H_2SO_4 | 8 | -8 K_2Cr_2O_7 | 2 | -2 CH_3CH_2OH | 3 | -3 H_2O | 11 | 11 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 2 | 2 CH_3CO_2H | 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 H_2SO_4 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 2 | -2 | -1/2 (Δ[K2Cr2O7])/(Δt) CH_3CH_2OH | 3 | -3 | -1/3 (Δ[CH3CH2OH])/(Δt) H_2O | 11 | 11 | 1/11 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 2 | 2 | 1/2 (Δ[Cr2(SO4)3])/(Δt) CH_3CO_2H | 3 | 3 | 1/3 (Δ[CH3CO2H])/(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 = -1/8 (Δ[H2SO4])/(Δt) = -1/2 (Δ[K2Cr2O7])/(Δt) = -1/3 (Δ[CH3CH2OH])/(Δt) = 1/11 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/2 (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[CH3CO2H])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium dichromate | ethanol | water | potassium sulfate | chromium sulfate | acetic acid formula | H_2SO_4 | K_2Cr_2O_7 | CH_3CH_2OH | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | CH_3CO_2H Hill formula | H_2O_4S | Cr_2K_2O_7 | C_2H_6O | H_2O | K_2O_4S | Cr_2O_12S_3 | C_2H_4O_2 name | sulfuric acid | potassium dichromate | ethanol | water | potassium sulfate | chromium sulfate | acetic acid IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | ethanol | water | dipotassium sulfate | chromium(+3) cation trisulfate | acetic acid