The hydrolysis of the sugar sucrose to the sugars glucose andfructose, C12H22O11+H2O⟶C6H12O6+C6H12O6 follows a first-order ratelaw for the disappearance of sucrose: rate = k[C12H22O11] (Theproducts of the reaction, glucose and fructose, have the samemolecular formulas but differ in the arrangement of the atoms intheir molecules.) (a) In neutral solution, k = 2.1 × 10−11 s−1 at27 °C and 8.5 × 10−11 s−1 at 37 °C. Determine the activationenergy, the frequency factor, and the rate constant for thisequation at 47 °C (assuming the kinetics remain consistent with theArrhenius equation at this temperature). (b) When a solution ofsucrose with an initial concentration of 0.150 M reachesequilibrium, the concentration of sucrose is 1.65 × 10−7 M. Howlong will it take the solution to reach equilibrium at 27 °C in theabsence of a catalyst? Because the concentration of sucrose atequilibrium is so low, assume that the reaction is irreversible.(c) Why does assuming that the reaction is irreversible simplifythe calculation in part (b)?
