CH3CH2OH + HCHO = H2O + CH3CH2CHO

CH_3CH_2OH ethanol + HCHO formaldehyde ⟶ H_2O water + CH_3COCH_3 acetone

Balance the chemical equation algebraically: CH_3CH_2OH + HCHO ⟶ H_2O + CH_3COCH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3CH_2OH + c_2 HCHO ⟶ c_3 H_2O + c_4 CH_3COCH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, H and O: C: | 2 c_1 + c_2 = 3 c_4 H: | 6 c_1 + 2 c_2 = 2 c_3 + 6 c_4 O: | c_1 + c_2 = c_3 + c_4 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CH_3CH_2OH + HCHO ⟶ H_2O + CH_3COCH_3

+ ⟶ +

ethanol + formaldehyde ⟶ water + acetone

Construct the equilibrium constant, K, expression for: CH_3CH_2OH + HCHO ⟶ H_2O + CH_3COCH_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 + HCHO ⟶ H_2O + CH_3COCH_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 HCHO | 1 | -1 H_2O | 1 | 1 CH_3COCH_3 | 1 | 1 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) HCHO | 1 | -1 | ([HCHO])^(-1) H_2O | 1 | 1 | [H2O] CH_3COCH_3 | 1 | 1 | [CH3COCH3] 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) ([HCHO])^(-1) [H2O] [CH3COCH3] = ([H2O] [CH3COCH3])/([CH3CH2OH] [HCHO])

Construct the rate of reaction expression for: CH_3CH_2OH + HCHO ⟶ H_2O + CH_3COCH_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 + HCHO ⟶ H_2O + CH_3COCH_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 HCHO | 1 | -1 H_2O | 1 | 1 CH_3COCH_3 | 1 | 1 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) HCHO | 1 | -1 | -(Δ[HCHO])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CH_3COCH_3 | 1 | 1 | (Δ[CH3COCH3])/(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) = -(Δ[HCHO])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CH3COCH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ethanol | formaldehyde | water | acetone formula | CH_3CH_2OH | HCHO | H_2O | CH_3COCH_3 Hill formula | C_2H_6O | CH_2O | H_2O | C_3H_6O name | ethanol | formaldehyde | water | acetone