At 345K , the half life for the decomposition of a sample of a...

$\dfrac{{\left({t}_{1/2}\right)}_{1}}{{\left({t}_{1/2}\right)}_{2}} = {\left(\dfrac{{P}_{1}}{{P}_{2}}\right)}^{1 - n}$

$⇒ \dfrac{340}{170} = {\left(\dfrac{55 . 5}{27 . 8}\right)}^{1 - n}$

${\left(2\right)}^{1} = {\left(2\right)}^{1 - n}$

$1 = 1 - n ⇒ n = 0$

For zero order reaction half life is directly proportional to the initial concentration.