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JEE Main levelSingle correct optionDifficulty 2 of 3ck137

A first-order reaction has $k = 1.5 \times 1 0^{- 3} s^{- 1}$ at 350 K and $E_{a} = 50 kJ mo l^{- 1}$ . With $R = 8.314 J mo l^{- 1} K^{- 1}$ , the pre-exponential factor in $s^{- 1}$ is

A $4.35 \times 1 0^{4}$
B $5.17 \times 1 0^{- 11}$
C $2.30 \times 1 0^{14}$
D $2.61 \times 1 0^{0}$

Answer: A

A = k e^{E_{a} / RT}

.

E_{a} / RT = \frac{50000}{8.314 \times 350} = 17.183

,

e^{17.183} = 28997525.5

, so

A = 1.5 \times 1 0^{- 3} \times 28997525.5 = 4.35 \times 1 0^{4} s^{- 1}

.

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