For a
first-order reaction, the rate law would be expressed as:
r = dC/dt = -kC
Integrating it from time zero and the initial
concentration, Co, to time, t, and the final concentration, C. We will
obtain the second-order integrated law as follows:
ln (C/Co) = -kt
To determine the time needed to change the concentration, we
simply substitute the given values from the problem statement as follows:
ln (C/Co) = -kt
ln (.78/1.00) = -1.42x10^-4 (t)
t = 1749.73 s
Therefore, the time it
takes to decrease the concentration of SO2Cl2 from 1.00 M to 0.78 M is
approximately 1749.72 s assuming that it follows a first - order reaction.
