99% of a 1st order reaction completed in 2.303minutes.What is the rate constant and half-life of the reaction

99% of a 1st order reaction completed in 2.303minutes.What is the rate constant and half-life of the reaction

A
2.303 and 0.3010
B
2 and 0.3465
C
2 and 0.693
D
0.3010 and 0.693

Solution:

For $1^{st}$ order reaction

$t_{99 %} = 2.303 \min then t_{1 / 2} ?$

$t_{99 %} = \frac{4.606}{K}$

$K = \frac{4.606}{t_{99 %}} = \frac{4.606}{2.303} = 2$

Then $t_{1 / 2} = \frac{0.693}{K} = \frac{0.693}{2} = 0.3465 \min$

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