(a) For first order reaction the integral rate law is:
kt=ln(‌

a0

a1

)
Given, ‌‌a0=1.6×10−2‌mol‌L−1
For t=300 s,‌‌at=0.8×10−2‌mol‌L−1
For t=600 s,‌‌at=0.4×10−2‌mol‌L−1
Using first set of data in the rate law,
k×300‌=ln‌

1.6×10−2

0.8×10−2

k‌=0.00231 s−1
Using second set of data in the rate law,
k×600‌=ln‌

1.6×10−2

0.4×10−2

k‌=0.00231 s−1
The value of k is consistent,therefore it follows first order reaction.
(b) The half-life of first order reaction is given by the following equation :
t1∕2‌=‌

ln‌2

k

=2.303×‌

log‌2

k

∴‌‌t1∕2‌=2.303×‌

log‌2

0.00231

=300.08 s.