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in Chemical Kinetics by (36.2k points)
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Derive the expression for the half-life of a chemical reaction of first order?

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For a first order reaction,

\(k=\frac{2.303}{t}log\frac{[R]_0}{[R]}\)

At  \(t_\frac{1}{2}\), [R] = \(\frac{[R]_0}{2}\) 

So, the above equation becomes,

\(k=\frac{2.303}{t}log\frac{[R]_0}{[R]/2}\) 

or, \(t_\frac{1}{2}\) = \(\frac{2.303}{k}log2\) 

\(t_\frac{1}{2}\) = \(\frac{2.303}{k}\times0.3010\) 

\(t_\frac{1}{2}\) = \(\frac{0.693}{k}\)

Thus, for a first order reaction, half-life period is constant, i.e., it is independent of initial concentration of the reacting species.

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