$A$ first order reaction has a rate constant $1.15 \times 10^{-3} \, s^{-1}$. How long will $5 \, g$ of this reactant take to reduce to $3 \, g$?

(N/A) For a first order reaction,the integrated rate equation is given by:
$t = \frac{2.303}{k} \log \frac{[R]_0}{[R]}$
Given:
Initial amount $[R]_0 = 5 \, g$
Final amount $[R] = 3 \, g$
Rate constant $k = 1.15 \times 10^{-3} \, s^{-1}$
Substituting the values:
$t = \frac{2.303}{1.15 \times 10^{-3}} \log \frac{5}{3}$
$t = \frac{2.303}{1.15 \times 10^{-3}} \times (\log 5 - \log 3)$
$t = \frac{2.303}{1.15 \times 10^{-3}} \times (0.6989 - 0.4771)$
$t = \frac{2.303}{1.15 \times 10^{-3}} \times 0.2218$
$t \approx 444.38 \, s$
Thus,the time taken is approximately $444 \, s$.