If compound A reacts with B following first order kinetics with rate constant $2.011 \times 10^{-3} \mathrm{~s}^{-1}$. 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 Main · 2023 · 30 Jan 2023 · Shift 1 · Chemical Kinetics

If compound A reacts with B following first order kinetics with rate constant

2.011 \times 1 0^{- 3} s^{- 1}

. The time taken by A (in seconds) to reduce from 7 g to 2 g will be ______. (Nearest Integer)

[lo g 5 = 0.698, lo g 7 = 0.845, lo g 2 = 0.301]

Answer: 623

For a first-order reaction the time is

t = \frac{2.303}{k} lo g \frac{[ A ] _{0}}{[ A ] _{t}}

. With the mass falling from

7 g

2 g

lo g \frac{7}{2} = lo g 7 - lo g 2 = 0.845 - 0.301 = 0.544

. Then

t = \frac{2.303}{2.011 \times 1 0 ^{- 3}} \times 0.544 \approx 623

. The time taken is about

623 s

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Integer answer