Answer:
[tex]\large \boxed{\text{D. 23.34 min}}[/tex]
Explanation:
1. Find the order of reaction
Use information from the graph to find the order.
If a plot of ln[A] vs time is linear, the reaction is first order and the slope = -k.
2. Find the half-life
[tex]k = \dfrac{\ln2}{ t_{\frac{1}{2}}}\\\\k = \text{-slope} = -(-2.97 \times 10^{-2} \text{ min}^{-1}) =2.97 \times 10^{-2} \text{ min}^{-1} \\ t_{\frac{1}{2}} =\dfrac{\ln 2}{k} = \dfrac{\ln 2}{2.97 \times 10^{-2}\text{ min}^{-1}} =\textbf{23.34 min}\\\\\text{The half-life is $\large \boxed{\textbf{23.34 min}}$}[/tex]
The half life of the reaction is 23.33 minutes.
We know that for a first order reaction;
ln[A]t = ln[A]o - kt
A plot of ln[A]t against time (t) will yield a straight line graph with a slope of -k.
From the question, the slope is -2.97 x 10-2 min-1.
So, -2.97 x 10-2 min-1 = - k
k = 2.97 x 10-2 min-1
The half life of a first order reaction is obtained from;
t1/2 = 0.693/k
t1/2 = 0.693/2.97 x 10-2 min-1
t1/2 = 23.33 minutes
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