The relationship between the half-life (t_{1/2}) and the rate constant (k) for a first-order reaction is given by the equation:
\[t_{1/2} = \frac{0.693}{k}\]
Rearranging this equation to solve for k, we get:
\[k = \frac{0.693}{t_{1/2}}\]
Substituting the given
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