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A first order reaction has a rate constant of $1.00\;s^{-1}$. What is the half life of the reaction?

$\begin{array}{1 1} 1.44 \;s \\ 0.693\;s \\ 2\;s \\ 1\;s \end{array}$

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Answer: 0.693 s
For a first order reaction only, the half life is a constant and is proportional to the inverse of the rate constant.
From the integrated rate law, we get $ [A] = [A]\; e^{-kt}$
Half-life is the time taken for the concentration of a reactant to drop to half its original value $[A] = \large\frac{[A_0]}{2}$
Substituting and taking lograthms on both sides, it can be shown that $t_{1/2} = \large\frac{ ln\;2}{k}$$ = \large\frac{0.693}{k}$
Given that $k = 1/s, \rightarrow t_{1/2} = 0.693\;s$
answered Jul 24, 2014 by balaji.thirumalai
 

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