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Chemistry · 2022 · 3 marks
CBSE 2022 · Region 1 · Set 1 · Q6
A first order reaction is 50% complete in 40 minutes. Calculate the time required for the completion of 90% of reaction. [Given: log 2=0.3010, log…
A first order reaction is $\displaystyle 50$% complete in $\displaystyle 40$ minutes. Calculate the time required for the completion of $\displaystyle 90$% of reaction.
[Given : $\displaystyle \log 2=0.3010, \log 10=1$ ]
Marking-scheme solution
\[\begin{aligned}
& \mathrm{t}_{1 / 2}=0.693 / \mathrm{k} \\
& \mathrm{k}=0.693 / \mathrm{t}_{1 / 2}=0.693 / 40 \mathrm{~min}^{-1}
\end{aligned}
\]
$\displaystyle 90$% completion
\[\begin{aligned}
\mathrm{t} & =2.303 / \mathrm{k} \log \left[\mathrm{R}_{0}\right] /[\mathrm{R}] \\
& =2.303 / 0.693 \times 40 \times \log 100 / 10 \\
& =2.303 / 0.693 \times 40=132.9 \mathrm{~min}
\end{aligned}
\]
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