A first order reaction has a specific reaction rate of $10^{-2} ext{ s}^{-1}$. How much time will it take fo

Question

A first order reaction has a specific reaction rate of $10^{-2} 	ext{ s}^{-1}$. How much time will it take for $20 	ext{ g}$ of the reactant to reduce to $5 	ext{ g}$?

Accepted Answer

For a first-order reaction, the time required is given by the integrated rate equation:

$t = \frac{2.303}{k} \log \frac{[R]_0}{[R]}$

Given data:
Rate constant, $k = 10^{-2} 	ext{ s}^{-1}$
Initial amount, $[R]_0 = 20 	ext{ g}$
Final amount, $[R] = 5 	ext{ g}$

Substituting the values into the equation:
$t = \frac{2.303}{10^{-2}} \log \left( \frac{20}{5} ight)$
$t = 2.303 	imes 10^2 	imes \log(4)$
$t = 230.3 	imes 2 \log(2)$
$t = 230.3 	imes 2 	imes 0.3010$
$t = 230.3 	imes 0.6020 \approx 138.64 	ext{ s}$

Therefore, the time required is approximately $138.6 	ext{ s}$.

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