Question

The gaseous reaction A₂ → 2A is first order in A₂. After 12.3 minutes 65% of A₂ remain undecomposed. How long will it take to decompose 90% of A₂? What is the half life of the reaction?

Answer 1

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Answer 2

Answer:

Time =1316.75 mins.

Half life = 198.11 mins.

Explanation:

Since we know the first order reaction $K = \dfrac{-2.303}{t} log\dfrac{R_{t} }{R_{0} }$.......................(1)

Initial condition  t = 12.3 min. 35% of A₂ is decomposed.

So, apply equation (1) we get,

$K = \dfrac{-2.303}{738}{log0.65}$

$K = -5.83 \times 10^{-4}$ (sec)^-1

For the second case 90% of A₂ is decomposed.

$-5.38\times 10^{-4} = \dfrac{-2.303}{t} {log0.01}$

So, t = 1316.75 mins.

We know that the half life is given by

$t_{\frac{1}{2} } =\dfrac{0.693}{k} = 198.11 mins.$