A first order reaction has a rate constant $\displaystyle 1.25 \times 10^{-3} \mathrm{~s}^{-1}$. How long will $\displaystyle 5$ g of this reactant take to reduce to $\displaystyle 2.5$ g ? $\displaystyle [\log 2=0 \cdot 301, \log 3=0 \cdot 4771, \log 4=0 \cdot 6021]$

\[\begin{aligned} & \mathrm{k}=\frac{2.303}{\mathrm{t}} \log \frac{[\mathrm{R}] \text { o }}{[\mathrm{R}]} \\ & \begin{aligned} 1.25 \times 10^{-3}=\frac{2.303}{\mathrm{t}} \log \left(\frac{5}{2.5}\right) & \\ & \mathrm{t}=\frac{2.303}{1.25 \times 10^{-3}} \log 2 \\ & \mathrm{t}=\frac{2 \cdot 303 \times 0.301}{1.25 \times 10^{-3}} \\ \mathrm{t}=554.5 \mathrm{~s} & \text { or } 5.54 \times 10^{2} \mathrm{~s} \end{aligned} \end{aligned} \]