CrO3 + CH3COCH3 = H2O + CO2 + Cr2O3

CrO_3 chromium trioxide + CH_3COCH_3 acetone ⟶ H_2O water + CO_2 carbon dioxide + Cr_2O_3 chromium(III) oxide

Balance the chemical equation algebraically: CrO_3 + CH_3COCH_3 ⟶ H_2O + CO_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CrO_3 + c_2 CH_3COCH_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 Cr, O, C and H: Cr: | c_1 = 2 c_5 O: | 3 c_1 + c_2 = c_3 + 2 c_4 + 3 c_5 C: | 3 c_2 = c_4 H: | 6 c_2 = 2 c_3 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 = 16/3 c_2 = 1 c_3 = 3 c_4 = 3 c_5 = 8/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 16 c_2 = 3 c_3 = 9 c_4 = 9 c_5 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 CrO_3 + 3 CH_3COCH_3 ⟶ 9 H_2O + 9 CO_2 + 8 Cr_2O_3

+ ⟶ + +

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

Construct the equilibrium constant, K, expression for: CrO_3 + CH_3COCH_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: 16 CrO_3 + 3 CH_3COCH_3 ⟶ 9 H_2O + 9 CO_2 + 8 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 CrO_3 | 16 | -16 CH_3COCH_3 | 3 | -3 H_2O | 9 | 9 CO_2 | 9 | 9 Cr_2O_3 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CrO_3 | 16 | -16 | ([CrO3])^(-16) CH_3COCH_3 | 3 | -3 | ([CH3COCH3])^(-3) H_2O | 9 | 9 | ([H2O])^9 CO_2 | 9 | 9 | ([CO2])^9 Cr_2O_3 | 8 | 8 | ([Cr2O3])^8 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 = ([CrO3])^(-16) ([CH3COCH3])^(-3) ([H2O])^9 ([CO2])^9 ([Cr2O3])^8 = (([H2O])^9 ([CO2])^9 ([Cr2O3])^8)/(([CrO3])^16 ([CH3COCH3])^3)

Construct the rate of reaction expression for: CrO_3 + CH_3COCH_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: 16 CrO_3 + 3 CH_3COCH_3 ⟶ 9 H_2O + 9 CO_2 + 8 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 CrO_3 | 16 | -16 CH_3COCH_3 | 3 | -3 H_2O | 9 | 9 CO_2 | 9 | 9 Cr_2O_3 | 8 | 8 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 CrO_3 | 16 | -16 | -1/16 (Δ[CrO3])/(Δt) CH_3COCH_3 | 3 | -3 | -1/3 (Δ[CH3COCH3])/(Δt) H_2O | 9 | 9 | 1/9 (Δ[H2O])/(Δt) CO_2 | 9 | 9 | 1/9 (Δ[CO2])/(Δt) Cr_2O_3 | 8 | 8 | 1/8 (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 = -1/16 (Δ[CrO3])/(Δt) = -1/3 (Δ[CH3COCH3])/(Δt) = 1/9 (Δ[H2O])/(Δt) = 1/9 (Δ[CO2])/(Δt) = 1/8 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium trioxide | acetone | water | carbon dioxide | chromium(III) oxide formula | CrO_3 | CH_3COCH_3 | H_2O | CO_2 | Cr_2O_3 Hill formula | CrO_3 | C_3H_6O | H_2O | CO_2 | Cr_2O_3 name | chromium trioxide | acetone | water | carbon dioxide | chromium(III) oxide IUPAC name | trioxochromium | acetone | water | carbon dioxide |