H2O + C12H22O11 = CO2 + CH3CH2OH

H_2O water + C_12H_22O_11 sucrose ⟶ CO_2 carbon dioxide + CH_3CH_2OH ethanol

Balance the chemical equation algebraically: H_2O + C_12H_22O_11 ⟶ CO_2 + CH_3CH_2OH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 C_12H_22O_11 ⟶ c_3 CO_2 + c_4 CH_3CH_2OH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and C: H: | 2 c_1 + 22 c_2 = 6 c_4 O: | c_1 + 11 c_2 = 2 c_3 + c_4 C: | 12 c_2 = c_3 + 2 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 = 4 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + C_12H_22O_11 ⟶ 4 CO_2 + 4 CH_3CH_2OH

+ ⟶ +

water + sucrose ⟶ carbon dioxide + ethanol

| water | sucrose | carbon dioxide | ethanol molecular enthalpy | -285.8 kJ/mol | -2226 kJ/mol | -393.5 kJ/mol | -277.7 kJ/mol total enthalpy | -285.8 kJ/mol | -2226 kJ/mol | -1574 kJ/mol | -1111 kJ/mol | H_initial = -2512 kJ/mol | | H_final = -2685 kJ/mol | ΔH_rxn^0 | -2685 kJ/mol - -2512 kJ/mol = -172.8 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: H_2O + C_12H_22O_11 ⟶ CO_2 + CH_3CH_2OH 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: H_2O + C_12H_22O_11 ⟶ 4 CO_2 + 4 CH_3CH_2OH 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_2O | 1 | -1 C_12H_22O_11 | 1 | -1 CO_2 | 4 | 4 CH_3CH_2OH | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) C_12H_22O_11 | 1 | -1 | ([C12H22O11])^(-1) CO_2 | 4 | 4 | ([CO2])^4 CH_3CH_2OH | 4 | 4 | ([CH3CH2OH])^4 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 = ([H2O])^(-1) ([C12H22O11])^(-1) ([CO2])^4 ([CH3CH2OH])^4 = (([CO2])^4 ([CH3CH2OH])^4)/([H2O] [C12H22O11])

Construct the rate of reaction expression for: H_2O + C_12H_22O_11 ⟶ CO_2 + CH_3CH_2OH 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: H_2O + C_12H_22O_11 ⟶ 4 CO_2 + 4 CH_3CH_2OH 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_2O | 1 | -1 C_12H_22O_11 | 1 | -1 CO_2 | 4 | 4 CH_3CH_2OH | 4 | 4 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_2O | 1 | -1 | -(Δ[H2O])/(Δt) C_12H_22O_11 | 1 | -1 | -(Δ[C12H22O11])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) CH_3CH_2OH | 4 | 4 | 1/4 (Δ[CH3CH2OH])/(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[H2O])/(Δt) = -(Δ[C12H22O11])/(Δt) = 1/4 (Δ[CO2])/(Δt) = 1/4 (Δ[CH3CH2OH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sucrose | carbon dioxide | ethanol formula | H_2O | C_12H_22O_11 | CO_2 | CH_3CH_2OH Hill formula | H_2O | C_12H_22O_11 | CO_2 | C_2H_6O name | water | sucrose | carbon dioxide | ethanol IUPAC name | water | (2R, 3S, 4S, 5S, 6R)-2-[(2S, 3S, 4S, 5R)-3, 4-dihydroxy-2, 5-bis(hydroxymethyl)oxolan-2-yl]oxy-6-(hydroxymethyl)oxane-3, 4, 5-triol | carbon dioxide | ethanol