# Calculate the half-life of a first order reaction from their rate constants given below:

Question:

Calculate the half-life of a first order reaction from their rate constants given below:

(i) 200 s−1 (ii) 2 min−1 (iii) 4 years−1

Solution:

(i) Half life, $t_{1 / 2}=\frac{0.693}{k}$

$=\frac{0.693}{200 \mathrm{~s}^{-1}}$

$=3.47 \times 10^{-3} \mathrm{~s}$ (approximately)

(ii) Half life, $t_{1 / 2}=\frac{0.693}{k}$

$=\frac{0.693}{2 \mathrm{~min}^{-1}}$

= 0.35 min (approximately)

(iii) Half life, $t_{1 / 2}=\frac{0.693}{k}$

$=\frac{0.693}{4 \text { years }^{-1}}$

= 0.173 years (approximately)