Question

The half life period of zero order reaction A ---> product is given by

Answer 1

T=[A°]/2K...........

Answer 2

Answer: $t_\frac{1}{2}=\frac{[a_0]}{2k}$

$A\rightarrow Products$

$rate=k[A]^0$    (1)

also $rate=-\frac{d[A]}{dt}$    (2)

equating 1 and 2  

$k=-\frac{d[A]}{dt}$       ($[A]^0=1)$

$kdt=-{d[A]}$

Integrating both sides and putting the limits for time as t=0 to t=t and for concentration from $[A]=[a_0]$ to $[A]=[a]$

Rate law expression for zero order kinetics is given by:

$kt=[a_0]-[a]$

$t=\frac{[a_0]-[a]}{k}$

where, t = time taken for decomposition

$[a_0]$ = initial concentration

$[a]$ = concentration left after time t

Half life period is the time taken to reduce the original reactants to half of its value.

$t=t_\frac{1}{2}$,  $[a]=\frac{[a_0]}{2}$

$t_\frac{1}{2}=\frac{[a_0]-\frac{[a_0]}{2}}{k}$

$t_\frac{1}{2}=\frac{[a_0]}{2k}$