In a first order reaction concentration of reactant decreases from \(20 \mathrm{~m} \mathrm{~mol}\) to \(10 \mathrm{~m} \mathrm{~mol}\) in \(1.151 \mathrm{~min}\). What is rate constant?

for 1st order reaction
\(\text { rate constant }(\mathrm{k})=\frac{2.303}{\ell} \log \frac{\mathrm{a}_{\mathrm{o}}}{\mathrm{a}_{\mathrm{t}}} \)
\( \mathrm{a}_{\mathrm{o}}=\text { Initial amount }=20 \mathrm{~m} \mathrm{~mol} \)
\( \text { at }=\text { final amount }=10 \mathrm{~m} \mathrm{~mol} \)
\( \mathrm{k}=\frac{2.303}{1.151} \cdot \log \frac{20}{10} \)
\( =\frac{2.303}{1.151} \times \log 2 \)
\( =\frac{2.303 \times .0 .3010}{1.151} \)
\( \mathrm{k}=0.60 \mathrm{~min}^{-1}\)
II \(^{\text {nd }}\) Method
As concentration decreases from \(20 \mathrm{~m} \mathrm{~mol}\) to \(10 \mathrm{~m} \mathrm{~mol}\) in \(1.151 \mathrm{~min}\) \(\ell_{1 / 2}=1.151 \mathrm{~min}=\frac{\ell \mathrm{n} 2}{\mathrm{~K}}\) \(\mathrm{k}=\frac{\ln 2}{1.151}=\frac{0.693}{1.151}\) \(\mathrm{k}=0.60 \mathrm{~min}^{-1}\)