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Half-Lives Of Order Of Reactions (t1/2)

  Half-Lives Of Order Of Reactions (t1/2)

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

Half-Lives Of Order Of Reactions (t1/2)

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

             Half-Lives Of Order Of Reactions (t1/2) e.q. 6.1

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

Half-Lives Of Order Of Reactions (t1/2)

As “2” and “K0” are constants so:

                                 t1/2 ∝ a                         e.q.6.2

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                                 

Half-Lives Of Order Of Reactions (t1/2)e.q.3.4

from this equation we can calculate half-life. As

         Half-Lives Of Order Of Reactions (t1/2)e.q. 6.3

At time t=0, initial concentration is “a”.

At time t= t1/2, the concentration will be  x = 1/2a (or 0.5a). Putting the value of t and x in e.q.6.3 we got

Half-Lives Of Order Of Reactions (t1/2)

As “0.693” and “K” are constants so:

                        t1/2=constant            e.q.6.4

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                

Half-Lives Of Order Of Reactions (t1/2) e.q.4.4

from this equation we can calculate half-life. As         

Half-Lives Of Order Of Reactions (t1/2)e.q. 6.5

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

Half-Lives Of Order Of Reactions (t1/2)

As “K” is constant so: Half-Lives Of Order Of Reactions (t1/2)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

Half-Lives Of Order Of Reactions (t1/2) e.q.5.2

from this equation we can calculate half-life. As

Half-Lives Of Order Of Reactions (t1/2)e.q. 6.7

At time t=0, initial concentration is “a”.

At time t= t1/2, the concentration will be  x = 1/2a (or 0.5a). Putting the value of t and x in e.q.6.7 we got

Half-Lives Of Order Of Reactions (t1/2)

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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