Half life of a chemical due to degradation

dC/dt = -k C

where :

C is the concentration of the chemical in mg/l or ppm

t= time - days

k= degradation constant

integrate differential equation

ò dC/C= -kò dt

over concentration Co to C1 and time to to t1

ln Cú ^{C1}= - k t ú ^{t1}

Co
to

At inital time to

ln C = -kt + ln Co

ln C/Co = - kt

C/Co = exp (-kt)

ln C/Co = -kt

half life C= Co/2

ln 1/2= -kt

time for half life

t= 0.693/k