C2H5OH + CrO3 = H2O + CO2 + Cr2O3

CH_3CH_2OH ethanol + CrO_3 chromium trioxide ⟶ H_2O water + CO_2 carbon dioxide + Cr_2O_3 chromium(III) oxide

Balance the chemical equation algebraically: CH_3CH_2OH + CrO_3 ⟶ H_2O + CO_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3CH_2OH + c_2 CrO_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, O and Cr: C: | 2 c_1 = c_4 H: | 6 c_1 = 2 c_3 O: | c_1 + 3 c_2 = c_3 + 2 c_4 + 3 c_5 Cr: | c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 3 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CH_3CH_2OH + 4 CrO_3 ⟶ 3 H_2O + 2 CO_2 + 2 Cr_2O_3

+ ⟶ + +

ethanol + chromium trioxide ⟶ water + carbon dioxide + chromium(III) oxide

| ethanol | chromium trioxide | water | carbon dioxide | chromium(III) oxide molecular free energy | -174.8 kJ/mol | -502 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -1058 kJ/mol total free energy | -174.8 kJ/mol | -2008 kJ/mol | -711.3 kJ/mol | -788.8 kJ/mol | -2116 kJ/mol | G_initial = -2183 kJ/mol | | G_final = -3616 kJ/mol | | ΔG_rxn^0 | -3616 kJ/mol - -2183 kJ/mol = -1434 kJ/mol (exergonic) | | | |

| ethanol | chromium trioxide | water | carbon dioxide | chromium(III) oxide molecular entropy | 160.7 J/(mol K) | 72 J/(mol K) | 69.91 J/(mol K) | 214 J/(mol K) | 81 J/(mol K) total entropy | 160.7 J/(mol K) | 288 J/(mol K) | 209.7 J/(mol K) | 428 J/(mol K) | 162 J/(mol K) | S_initial = 448.7 J/(mol K) | | S_final = 799.7 J/(mol K) | | ΔS_rxn^0 | 799.7 J/(mol K) - 448.7 J/(mol K) = 351 J/(mol K) (endoentropic) | | | |

Construct the equilibrium constant, K, expression for: CH_3CH_2OH + CrO_3 ⟶ H_2O + CO_2 + Cr_2O_3 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: CH_3CH_2OH + 4 CrO_3 ⟶ 3 H_2O + 2 CO_2 + 2 Cr_2O_3 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 CH_3CH_2OH | 1 | -1 CrO_3 | 4 | -4 H_2O | 3 | 3 CO_2 | 2 | 2 Cr_2O_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CH_3CH_2OH | 1 | -1 | ([CH3CH2OH])^(-1) CrO_3 | 4 | -4 | ([CrO3])^(-4) H_2O | 3 | 3 | ([H2O])^3 CO_2 | 2 | 2 | ([CO2])^2 Cr_2O_3 | 2 | 2 | ([Cr2O3])^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 = ([CH3CH2OH])^(-1) ([CrO3])^(-4) ([H2O])^3 ([CO2])^2 ([Cr2O3])^2 = (([H2O])^3 ([CO2])^2 ([Cr2O3])^2)/([CH3CH2OH] ([CrO3])^4)

Construct the rate of reaction expression for: CH_3CH_2OH + CrO_3 ⟶ H_2O + CO_2 + Cr_2O_3 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: CH_3CH_2OH + 4 CrO_3 ⟶ 3 H_2O + 2 CO_2 + 2 Cr_2O_3 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 CH_3CH_2OH | 1 | -1 CrO_3 | 4 | -4 H_2O | 3 | 3 CO_2 | 2 | 2 Cr_2O_3 | 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 CH_3CH_2OH | 1 | -1 | -(Δ[CH3CH2OH])/(Δt) CrO_3 | 4 | -4 | -1/4 (Δ[CrO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) Cr_2O_3 | 2 | 2 | 1/2 (Δ[Cr2O3])/(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 = -(Δ[CH3CH2OH])/(Δt) = -1/4 (Δ[CrO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ethanol | chromium trioxide | water | carbon dioxide | chromium(III) oxide formula | CH_3CH_2OH | CrO_3 | H_2O | CO_2 | Cr_2O_3 Hill formula | C_2H_6O | CrO_3 | H_2O | CO_2 | Cr_2O_3 name | ethanol | chromium trioxide | water | carbon dioxide | chromium(III) oxide IUPAC name | ethanol | trioxochromium | water | carbon dioxide |