1. Tardigrade
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  3. Chemistry
  4. If compound A reacts with B following first order kinetics with rate constant 2.011 × 10-3 s -1. The time taken by A (in seconds) to reduce from 7 g to 2 g will be (Nearest Integer) [ log 5=0.698, log 7=0.845, log 2=0.301]

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Q. If compound $A$ reacts with $B$ following first order kinetics with rate constant $2.011 \times 10^{-3} s ^{-1}$. The time taken by $A$ (in seconds) to reduce from $7\, g$ to $2\, g$ will be ______ (Nearest Integer)
$[\log 5=0.698, \log 7=0.845, \log 2=0.301]$

JEE MainJEE Main 2023Chemical Kinetics

Solution:

image
at constant volume
$t =\frac{2.303}{ K } \log \frac{[ A ]_0}{[ A ]_{ t }}$
$ =\frac{2.303}{2 \cdot 011 \times 10^{-3}} \log \frac{7}{2} $
$=\frac{2 \cdot 303 \times 0 \cdot 544}{2 \cdot 011 \times 10^{-3}} $
$ =622.989 $
$ \approx 623$