Question

5. Sucrose is readily hydrolysed to glucose and fructose in acidic solution. The hydrolysis is often monitored by measuring the angle of rotation of plane-polarized light passing through the solution. From the angle of rotation the concentration of sucrose can be determined. An experiment on the hydrolysis of sucrose in 0.50m HCl(aq) produced the following data: t/min 0 14 39 60 80 110 140 170 210 [sucrose] 0.316 0.300 0.274 0.256 0.238 0.211 0.190 0.170 0.146 Determine the rate constant of the reaction and the half-life of a sucrose molecule.

Answer 1

ln a = −1.1491 − 3.6697 × 10−3t

Explanation:

The first order integrated rate law is

kt = ln (a0/a)

ln a=ln a0 − kt

A plot of ln(a) vs. t would, therefore, yield a straight line whose slope will be equal to −k. The result of the linear regression (Excel can easily do this) is

ln a = −1.1491 − 3.6697 × 10−3t

Therefore, the rate constant is 3.6697 × 10−3 s−1. Note that the intercept has approximately the correct value of ln a0.