C3H8O3 = H2O + C3H4O

HOCH_2CH(OH)CH_2OH glycerol ⟶ H_2O water + CH_2=CHCHO acrolein

Balance the chemical equation algebraically: HOCH_2CH(OH)CH_2OH ⟶ H_2O + CH_2=CHCHO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HOCH_2CH(OH)CH_2OH ⟶ c_2 H_2O + c_3 CH_2=CHCHO Set the number of atoms in the reactants equal to the number of atoms in the products for C, H and O: C: | 3 c_1 = 3 c_3 H: | 8 c_1 = 2 c_2 + 4 c_3 O: | 3 c_1 = c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HOCH_2CH(OH)CH_2OH ⟶ 2 H_2O + CH_2=CHCHO

⟶ +

glycerol ⟶ water + acrolein

Construct the equilibrium constant, K, expression for: HOCH_2CH(OH)CH_2OH ⟶ H_2O + CH_2=CHCHO 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: HOCH_2CH(OH)CH_2OH ⟶ 2 H_2O + CH_2=CHCHO 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 HOCH_2CH(OH)CH_2OH | 1 | -1 H_2O | 2 | 2 CH_2=CHCHO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HOCH_2CH(OH)CH_2OH | 1 | -1 | ([HOCH2CH(OH)CH2OH])^(-1) H_2O | 2 | 2 | ([H2O])^2 CH_2=CHCHO | 1 | 1 | [CH2=CHCHO] 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 = ([HOCH2CH(OH)CH2OH])^(-1) ([H2O])^2 [CH2=CHCHO] = (([H2O])^2 [CH2=CHCHO])/([HOCH2CH(OH)CH2OH])

Construct the rate of reaction expression for: HOCH_2CH(OH)CH_2OH ⟶ H_2O + CH_2=CHCHO 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: HOCH_2CH(OH)CH_2OH ⟶ 2 H_2O + CH_2=CHCHO 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 HOCH_2CH(OH)CH_2OH | 1 | -1 H_2O | 2 | 2 CH_2=CHCHO | 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 HOCH_2CH(OH)CH_2OH | 1 | -1 | -(Δ[HOCH2CH(OH)CH2OH])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CH_2=CHCHO | 1 | 1 | (Δ[CH2=CHCHO])/(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[HOCH2CH(OH)CH2OH])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[CH2=CHCHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| glycerol | water | acrolein formula | HOCH_2CH(OH)CH_2OH | H_2O | CH_2=CHCHO Hill formula | C_3H_8O_3 | H_2O | C_3H_4O name | glycerol | water | acrolein IUPAC name | glycerol | water | prop-2-enal

| glycerol | water | acrolein molar mass | 92.09 g/mol | 18.015 g/mol | 56.064 g/mol phase | liquid (at STP) | liquid (at STP) | liquid (at STP) melting point | 20 °C | 0 °C | -87 °C boiling point | 182 °C (measured at 2666 Pa) | 99.9839 °C | 53 °C density | 1.25 g/cm^3 | 1 g/cm^3 | 0.839 g/cm^3 solubility in water | miscible | | surface tension | 0.0648 N/m | 0.0728 N/m | 0.024 N/m dynamic viscosity | 0.934 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | 3.5×10^-4 Pa s (at 20 °C) odor | odorless | odorless | piercing | disagreeable