Question

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

1.  \(200\  s^{-1 }\)
2. \(2 \ min^{-1 }\)
3. \(4\  years^{-1}\)

Answer 1

\((i)\) \(Half \ life\) \(t_{\frac 12} = \frac {0.693}{k}\)

= \(\frac {0.693}{200\ s^{-1}} \)

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

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\((ii)\) \(Half \ life\)  \(t_{\frac 12} = \frac {0.693}{k}\)

=\(\frac { 0.693}{2 \ min^{-1}}\)

= \(0.35 \ min \  (approximately)\)

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\((iii)\) \(Half \ life\)  \(t_{\frac 12} = \frac {0.693}{k}\)

= \(\frac {0.693}{4 \ year^{-1}}\)

= \(0.173\  years\   (approximately)\)