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JEE Advanced levelSingle correct optionDifficulty 3 of 3ck155

A first-order reaction has a half-life of 40 min at 300 K and $E_{a} = 50 kJ mo l^{- 1}$ ( $R = 8.314 J mo l^{- 1} K^{- 1}$ ). The time (in min) for 87.5% completion at 320 K is

A11.4
B34.3
C420.1
D45.7

Answer: B

ln (k_{320} / k_{300}) = \frac{50000}{8.314} (0.000208) = 1.253

, ratio

3.50

. So

t_{1/2} (320) = 40/3.50 = 11.43

min. 87.5% completion is three half-lives:

t = 34.3

min.

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