For the first-order reaction below,the initial concentration of A is 0.80 M.What is the half-life of the reaction if the concentration of A decreases to 0.10 M in 54 seconds? $ \mathrm{A} \rightarrow \mathrm{B} $$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$rate $ =k[\mathrm{~A}] $

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For a first-order reaction, the half-life ($t_{1/2}$) is given by $t_{1/2} = \frac{0.693}{k}$, where $k$ is the rate constant. The half-life is independent of the initial concentration. Since the concentration decreases from 0.80 M to 0.10 M in 54 seconds, it goes through three half-lives (0.80 M to 0.40 M, 0.40 M to 0.20 M, and 0.20 M to 0.10 M). Therefore, $54 \, \text{seconds} / 3 = 18 \, \text{seconds}$ per half-life.

For the First-Order Reaction Below,the Initial Concentration of a Is A→B \mathrm{A} \rightarrow \mathrm{B} A→B

For the First-Order Reaction Below,the Initial Concentration of a Is $\mathrm{A} \rightarrow \mathrm{B}$