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First Order Reaction

The t1/2 of...

Question

The $t_{1 / 2}$ of first order reaction is $60$ minutes. What percentage will be left after $240$ minutes?

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Solution

$k = \frac{2.303}{t} l o g \frac{A_{o}}{A_{t}}$
$t = \frac{2.303}{0.693 / 60} l o g \frac{A_{o}}{A_{t}}$
$240 = \frac{2.303}{0.693 / 60} l o g \frac{A_{o}}{A_{t}}$
$\frac{240 \times 0.639}{2.303 \times 60} = l o g \frac{A_{o}}{A_{t}}$
$l o g \frac{A_{o}}{A_{t}} = 1.2036$
Suppose $A_{o} = 100$
$A_{t} = 6.25$ .

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