H2O + C12H22O11 = C6H12O6

H_2O water + C_12H_22O_11 sucrose ⟶ C_6H_12O_6 D-(+)-glucose

Balance the chemical equation algebraically: H_2O + C_12H_22O_11 ⟶ C_6H_12O_6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 C_12H_22O_11 ⟶ c_3 C_6H_12O_6 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 = 12 c_3 O: | c_1 + 11 c_2 = 6 c_3 C: | 12 c_2 = 6 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 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + C_12H_22O_11 ⟶ 2 C_6H_12O_6

+ ⟶

water + sucrose ⟶ D-(+)-glucose

Construct the equilibrium constant, K, expression for: H_2O + C_12H_22O_11 ⟶ C_6H_12O_6 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 ⟶ 2 C_6H_12O_6 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 C_6H_12O_6 | 2 | 2 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) C_6H_12O_6 | 2 | 2 | ([C6H12O6])^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 = ([H2O])^(-1) ([C12H22O11])^(-1) ([C6H12O6])^2 = ([C6H12O6])^2/([H2O] [C12H22O11])

Construct the rate of reaction expression for: H_2O + C_12H_22O_11 ⟶ C_6H_12O_6 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 ⟶ 2 C_6H_12O_6 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 C_6H_12O_6 | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) C_12H_22O_11 | 1 | -1 | -(Δ[C12H22O11])/(Δt) C_6H_12O_6 | 2 | 2 | 1/2 (Δ[C6H12O6])/(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) = 1/2 (Δ[C6H12O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sucrose | D-(+)-glucose formula | H_2O | C_12H_22O_11 | C_6H_12O_6 name | water | sucrose | D-(+)-glucose 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 | 6-(hydroxymethyl)oxane-2, 3, 4, 5-tetrol

| water | sucrose | D-(+)-glucose molar mass | 18.015 g/mol | 342.3 g/mol | 180.16 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | 170 °C | 146 °C boiling point | 99.9839 °C | | density | 1 g/cm^3 | 1.59 g/cm^3 | 1.54 g/cm^3 solubility in water | | | soluble surface tension | 0.0728 N/m | 0.0622 N/m | 0.07173 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 0.56 Pa s (at 145 °C) odor | odorless | |