Verified Solution • 2025–26 Session moderate

QJEEM22Ch269c: JEE Main 2022 Chemistry - Class 12 JEEM22Ch269c Solution: For the given first order reaction the half life of the…

For the given first order reaction

A→B\mathrm{A} \rightarrow \mathrm{B}

the half life of the reaction is 0.3010 min0.3010 \mathrm{~min} . The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min2.0 \mathrm{~min} will be equal to ___________. (Nearest integer)

Step-by-Step Verified Solution

t1/2=0.693 Kt1/2\mathrm{t}_{1 / 2}=\frac{0.693}{\mathrm{~K}} \quad\quad \mathrm{t}_{1 / 2} given =0.3010=0.3010

amp;K=0.6930.3010amp;K=2.30\begin{aligned}&K=\frac{0.693}{0.3010} \\\\&K=2.30\end{aligned}

K=2.303tlog⁡(A0)(At)\mathrm{K}=\frac{2.303}{\mathrm{t}} \log \frac{\left(\mathrm{A}_{0}\right)}{\left(\mathrm{A}_{\mathrm{t}}\right)}

A0→A_{0} \rightarrow initial concentration of reactant

At→A_{t} \rightarrow concentration of reactant at time tt

2.303=2.3032log⁡(A0)(At)2.303=\frac{2.303}{2} \log \frac{\left(A_{0}\right)}{\left(A_{t}\right)}

2=log⁡(A0)(At)2=\log \frac{\left(A_{0}\right)}{\left(A_{t}\right)}

100=A0At100=\frac{A_{0}}{A_{t}}

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