Half-Lives Of Order Of Reactions (t1/2)
Time in which
half of the reactants are converted into products is known as half-life.
General
equation for half-life is
where n=
order of reaction
6.1 Half-life of Zero order reaction
We know that
rate equation for zero order reaction is
x = K0
t
e.q.2.4
from this
equation we can calculate half-life. As
At time t=0, initial
concentration is “a”.
At time t= t1/2, the concentration will be . Putting the value of t and x in e.q.2.4 we got
As “2” and “K0” are constants so:
t1/2
E.q.6.2 indicates that half-life for zero order reaction depends
directly on the initial concentration of reactants.
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6.2 Half-life of first order reaction
We know that
rate equation for first order reaction is
from this
equation we can calculate half-life. As
At time t=0, initial concentration is “a”.
At time t= t1/2, the concentration will be
As “0.693” and “K” are constants so:
t1/2=constant
E.q.6.4 indicates that half-life for first order reaction is
independent of the initial concentration of reactants.
6.3 Half-life of second order reaction
We know that rate equation for second order reaction is
from this equation we can calculate half-life. As
At time t=0, initial
concentration is “a”.
At time t= t1/2, the concentration will be x = /2a (or 0.5a). Putting the value of t and x in e.q.6.5 we got
As “K” is constant so: e.q.6.6
E.q.6.6 indicates that
half-life for second order reaction is inversely proportional to the initial
concentration of reactants.
6.4 Half-life of third order reaction
We know that
rate equation for third order reaction is
from this
equation we can calculate half-life. As
At time t=0, initial
concentration is “a”.
At time t= t1/2, the concentration will be
As “K” and “1.5” are constants so, e.q.6.8
E.q.6.8 indicates that
half-life for third order reaction is inversely proportional to the square of initial
concentration of reactants.
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