AMU Engineering 2018 solved paper Solved Paper

Integrated rate law for the second order reaction is

1

[A]t

=

1

[A]0

+kt ........(i)
For half-life time t=t1∕2,[A]t=[A]0∕2
On putting the values in Eq. (i)

1

[A]t∕2

=

1

[A]0

+kt1∕2
kt1∕2=

2

[A]0

−

1

[A]0

t1∕2=

1

k

[

1

[A]0

] ...........(ii)
For three quarter half-life time t=t3∕4,[A]t=[A]0∕4
On putting the values in Eq. (i)

1

[A]0∕4

=

1

[A]0

+kt3∕4
t3∕4=

1

k

[

3

[A]0

] ..........(iii)
Now, ratio of t1∕2 to t3∕4 is given by

t1∕2

t3∕4

=

1 k [ 1 [A]0 ]

1 k [ 3 [A]0 ]

t1∕2:t3∕4=1:3
Hence, t1∕2:t3∕4 is independent of the concentration of reactant.