The decomposition of so2cl2 is first order in so2cl2 and has a rate constant of 1.42 x 10^-4 if the initial concentration of so2cl2 is 1.00 m how long will it take for the concentration to decrease to. 78 m

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.