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The reaction $A \to B$ follows first order kinetics. The time taken for 0.8 mole of A to produce 0.6 moles of B in 1 hour. What is the time taken for conversion of 0.9 mole of A to produces 0.675 moles of B?

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2 hours

0.5 hour

1 hour

0.25 hours

answer is A.

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Detailed Solution

$A \to B A \to B$

$t = 0 0.8 0 t = 0 0.9 0$

$t = t 0.2 0.6 t = t 0.225 0.675$

$K_{1} = K_{2}$

$\frac{2.303}{1} \log [\frac{0.8}{0.2}] = \frac{2.303}{x} \log [\frac{0.9}{0.225}]$

$x = 1 hr$

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