If the rate constant for a first order reaction is 2 . 303 × 10 - 3 s - 1 , find the time required to reduce…
If the rate constant for a first order reaction is , find the time required to reduce of the reactant to .
Solution
Given:
- Rate constant, \(k=2.303 \times 10^{-3} \mathrm{~s}^{-1}\) for a first-order reaction.
- Initial concentration of the reactant, \([A]_0=4 \mathrm{~g}\).
- Final concentration of the reactant, \([A]=0.2 \mathrm{~g}\).
We want to find the time required to reduce \(4 \mathrm{~g}\) of the reactant to \(0.2 \mathrm{~g}\).
Using the first-order reaction kinetics formula:
\(\ln \left(\frac{[A]}{[A]_0}ight)=-k t\)
Substituting the given values:
\(\ln \left(\frac{0.2}{4}ight)=-\left(2.303 \times 10^{-3}ight) \cdot t\)
Solving for \(t\) :
\(\begin{aligned}
& t=\frac{-\ln (20)}{-2.303 \times 10^{-3}} \\
& t \approx \frac{2.9957}{2.303 \times 10^{-3}} \\
& t \approx 1300 \mathrm{~s}
\end{aligned}\)
Converting to hours:
\(1300 \mathrm{~s} \times \frac{1 \text { hour }}{3600 \mathrm{~s}} \approx 0.361 \text { hours }\)
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