Q7 of 26 Page 1

Show that in a first order reaction, time required for completion of 99.9% is 10 times that of half-life (t1/2) of the reaction.

OR


Derive integrated rate equation for rate constant for a first order reaction.


Given, order of reaction, n = 1


Initial concentration = [Ro]


Final concentration after 99.9% completion of reaction,


[R] = [Ro] - [Ro]


[R] = [Ro]


We know, K = log


K = log


K = log(103)


K = …(1)


Now, we also know, K = …(2)


Comparing 1 and 2, we get,


=


t = 10 t1/2


OR


Consider the reaction, R → P


For 1st order kinetics, rate =


On rearranging,


Integrating both the sides,


ln [R] = -kt + I …(1)


Substituting the limits i.e. when t = 0, [R] = [Ro]


ln [R0] = I


Putting above equation in (1), we get


ln [R] = -kt + ln [R0]


ln [R] – ln [Ro] = -kt


ln [R0] – ln [R] = kt


ln = kt


k = log


where, [R] = final concentration after time t


[Ro] = initial concentration


K = rate constant (sec-1)


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