What time is required for 100 g of reactant to reduce to 25 g in a first order reaction having half life 5760 year?

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Aicharya · Accepted Answer

For a first order reaction, $\begin{aligned} & {\left[\mathrm{A}_0ight]=100 \mathrm{~g} ;\left[\mathrm{A}_{\mathrm{t}}ight]=25 \mathrm{~g} ; \mathrm{t}_{1 / 2}=5760 	ext { years } } \ & \mathrm{k}=\frac{0.693}{\mathrm{t}_{1 / 2}}=\frac{0.693}{5760 \mathrm{yr}}=1.203 	imes 10^{-4} 	ext { year }^{-1} \ & \mathrm{t}=\frac{2.303}{\mathrm{k}} \log _{10} \frac{\left[\mathrm{~A}_0ight]}{\left[\mathrm{A}_{\mathrm{t}}ight]} \ 	herefore \quad & \mathrm{t}=\frac{2.303}{1.203 	imes 10^{-4} 	ext { year }^{-1}} \log _{10} \frac{100}{25} \ & =19141.8 	imes 0.6021=11526.5 	ext { years } \end{aligned}$

What time is required for 100 g of reactant to reduce to 25 g in a first order reaction having half life…

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