Question

please solve it step by step​

Answer 1

Zero order reaction:

$\rm A(g) \longrightarrow B(g) + C(g)$

Completion time for the zero order reaction (t) = 13.86 min

Half life of zero order reaction:

$\rm {(t_{1/2})}_{zero \: order} = \dfrac{t}{2} \\ \\ \rm {(t_{1/2})}_{zero \: order} = \dfrac{13.86}{2} \\ \\ \rm {(t_{1/2})}_{zero \: order} = 6.93$

First order reaction:

$\rm X(g) \longrightarrow Y(g)$

Half life of first order reaction:

$\rm {(t_{1/2})}_{first \: order} = \dfrac{ln 2}{k}$

According to the question, Half life for the zero order reaction and half life for the first order reaction are equal.

$\rm \leadsto {(t_{1/2})}_{zero \: order} = {(t_{1/2})}_{first \: order} \\ \\ \rm \leadsto 6.93 = \dfrac{ln2}{k} \\ \\ \rm \leadsto k = \dfrac{ln2}{6.93} \\ \\ \rm \leadsto k = \dfrac{0.693}{6.93} \\ \\ \rm \leadsto k = 0.1 \: min^{ - 1} \\ \\ \rm \leadsto k = 6 \: hr^{ - 1}$

$\therefore$ Rate constant for reaction X(g) → Y(g) = 6 $\sf hr^{-1}$

Answer 2

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