Chapter 13, Problem 97E

The hydrolysis of the sugar sucrose to the sugars glucose and fructose follows a first-order rate equation for the disappearance of sucrose.

${\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}\left(aq\right)+{\text{H}}_2\text{O}\left(l\right)\to {\text{C}}_6{\text{H}}_{12}{\text{O}}_6\left(aq\right)+{\text{C}}_6{\text{H}}_{12}{\text{O}}_6\left(aq\right)$

Rate $=k\left[{\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}\right]$

In neutral solution, $k=2.1\times {10}^{-11}$ at 27 °C. (As indicated by the rate constant, this is a very slow reaction. In the human body, the rate of this reaction is sped up by a type of catalyst called an enzyme.) (Note: That is not a mistake in the equation—the products of the reaction, glucose and fructose, have the same molecular formulas, ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$, but differ in the arrangement of the atoms in their molecules). The equilibrium constant for the reaction is $1.36\times {10}^5$ at 27 °C. What are the concentrations of glucose, fructose, and sucrose after a 0.150 M aqueous solution of sucrose has reached equilibrium? Remember that the activity of a solvent (the effective concentration) is 1.