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# A certain first order reaction is 45% complete in 65 seconds. Determine the rate constant and the half-life for this process.

$\begin{array}{1 1} 75.4 \;s \\ 37.7\;s \\ 17.8 \;s \\ 100.4 \;s \end{array}$

Before we calculate the half-life, we need to calculate $k$ the rate constant in order to get the half-life.
Given 45% reacted $\rightarrow$ 55% remains:
$ln\;A = -kt + ln\;A_0 \rightarrow ln 0.55 = -k \times 45\;s + ln \; 1 \rightarrow k - 0.0091975s^{-1}$
For a first order reaction, $t_{1/2} = \large\frac{ln\;2}{k}$$=\large\frac{0.693}{0.0091975}$$s = 75.4\;s$