H2SO4 + C2H5OH + Na2Cr2O7 = H2O + Na2SO4 + Cr2(SO4)3 + CH3COH

H_2SO_4 sulfuric acid + CH_3CH_2OH ethanol + Na_2Cr_2O_7 sodium bichromate ⟶ H_2O water + Na_2SO_4 sodium sulfate + Cr_2(SO_4)_3 chromium sulfate + CH_3CHO acetaldehyde

Balance the chemical equation algebraically: H_2SO_4 + CH_3CH_2OH + Na_2Cr_2O_7 ⟶ H_2O + Na_2SO_4 + Cr_2(SO_4)_3 + CH_3CHO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 CH_3CH_2OH + c_3 Na_2Cr_2O_7 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 CH_3CHO Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, C, Cr and Na: H: | 2 c_1 + 6 c_2 = 2 c_4 + 4 c_7 O: | 4 c_1 + c_2 + 7 c_3 = c_4 + 4 c_5 + 12 c_6 + c_7 S: | c_1 = c_5 + 3 c_6 C: | 2 c_2 = 2 c_7 Cr: | 2 c_3 = 2 c_6 Na: | 2 c_3 = 2 c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 1 c_4 = 7 c_5 = 1 c_6 = 1 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 3 CH_3CH_2OH + Na_2Cr_2O_7 ⟶ 7 H_2O + Na_2SO_4 + Cr_2(SO_4)_3 + 3 CH_3CHO

+ + ⟶ + + +

sulfuric acid + ethanol + sodium bichromate ⟶ water + sodium sulfate + chromium sulfate + acetaldehyde

Construct the equilibrium constant, K, expression for: H_2SO_4 + CH_3CH_2OH + Na_2Cr_2O_7 ⟶ H_2O + Na_2SO_4 + Cr_2(SO_4)_3 + CH_3CHO 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: 4 H_2SO_4 + 3 CH_3CH_2OH + Na_2Cr_2O_7 ⟶ 7 H_2O + Na_2SO_4 + Cr_2(SO_4)_3 + 3 CH_3CHO 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 | 4 | -4 CH_3CH_2OH | 3 | -3 Na_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 Na_2SO_4 | 1 | 1 Cr_2(SO_4)_3 | 1 | 1 CH_3CHO | 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 | 4 | -4 | ([H2SO4])^(-4) CH_3CH_2OH | 3 | -3 | ([CH3CH2OH])^(-3) Na_2Cr_2O_7 | 1 | -1 | ([Na2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 Na_2SO_4 | 1 | 1 | [Na2SO4] Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] CH_3CHO | 3 | 3 | ([CH3CHO])^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])^(-4) ([CH3CH2OH])^(-3) ([Na2Cr2O7])^(-1) ([H2O])^7 [Na2SO4] [Cr2(SO4)3] ([CH3CHO])^3 = (([H2O])^7 [Na2SO4] [Cr2(SO4)3] ([CH3CHO])^3)/(([H2SO4])^4 ([CH3CH2OH])^3 [Na2Cr2O7])

Construct the rate of reaction expression for: H_2SO_4 + CH_3CH_2OH + Na_2Cr_2O_7 ⟶ H_2O + Na_2SO_4 + Cr_2(SO_4)_3 + CH_3CHO 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: 4 H_2SO_4 + 3 CH_3CH_2OH + Na_2Cr_2O_7 ⟶ 7 H_2O + Na_2SO_4 + Cr_2(SO_4)_3 + 3 CH_3CHO 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 | 4 | -4 CH_3CH_2OH | 3 | -3 Na_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 Na_2SO_4 | 1 | 1 Cr_2(SO_4)_3 | 1 | 1 CH_3CHO | 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) CH_3CH_2OH | 3 | -3 | -1/3 (Δ[CH3CH2OH])/(Δt) Na_2Cr_2O_7 | 1 | -1 | -(Δ[Na2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) CH_3CHO | 3 | 3 | 1/3 (Δ[CH3CHO])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/3 (Δ[CH3CH2OH])/(Δt) = -(Δ[Na2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[CH3CHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | ethanol | sodium bichromate | water | sodium sulfate | chromium sulfate | acetaldehyde formula | H_2SO_4 | CH_3CH_2OH | Na_2Cr_2O_7 | H_2O | Na_2SO_4 | Cr_2(SO_4)_3 | CH_3CHO Hill formula | H_2O_4S | C_2H_6O | Cr_2Na_2O_7 | H_2O | Na_2O_4S | Cr_2O_12S_3 | C_2H_4O name | sulfuric acid | ethanol | sodium bichromate | water | sodium sulfate | chromium sulfate | acetaldehyde IUPAC name | sulfuric acid | ethanol | disodium oxido-(oxido-dioxo-chromio)oxy-dioxo-chromium | water | disodium sulfate | chromium(+3) cation trisulfate | acetaldehyde