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JEE Main 202124 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
24 February
Shift
Evening Shift
Subject
Chemistry
Chapter
Chemical Kinetics

JEE Main 2021 · 24 February · Evening Shift · Chemistry · Chemical Kinetics

Sucrose hydrolyses in acid solution into glucose and fructose...

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33h3 . 33h at 25°C.25 ° C . After 9h,9h, the fraction of sucrose remaining is f.f . The value of log⁡10\log_{10}\left(\dfrac{1}{f}\right)is ________\times {10}^{- 2} .(Roundedofftothenearestinteger)</p><p>[Assume:In(Rounded off to the nearest integer)</p><p>[Assume: In10 = 2 . 303, \ln 2 = 0 . 693]

Correct answer

0

Step-by-step solution

C12H22O11+H2O→t1/2=103hrorderC6H12O6Glucose+C6H12O6Fructose{C}_{12}{H}_{22}{O}_{11} + {H}_{2}O\mathop{\to}_{{t}_{1/2} = \dfrac{10}{3}hr}^{order}\mathop{{C}_{6}{H}_{12}{O}_{6}}_{Glucose} + \mathop{{C}_{6}{H}_{12}{O}_{6}}_{Fructose}

t=0a=[A]0t = 0a = {\left[A\right]}_{0}

t=9hra−x=[A]tt = 9hra - x = {\left[A\right]}_{t}

from I order kinetic: k×t2.303=log∣A∣0∣A∣t\dfrac{k \times t}{2 . 303} = log\dfrac{{\left|A\right|}_{0}}{{\left|A\right|}_{t}}

⇒ln⁡2×9103×2.303=log⁡(1f)⇒ \dfrac{\ln 2 \times 9}{\dfrac{10}{3} \times 2 . 303} = \log \left(\dfrac{1}{f}\right)

⇒0.693×9×323.03=log⁡(1f)⇒ \dfrac{0 . 693 \times 9 \times 3}{23 . 03} = \log \left(\dfrac{1}{f}\right)

⇒log⁡(1f)=0.81246=81.24×10−2⇒ \log \left(\dfrac{1}{f}\right) = 0 . 81246 = 81 . 24 \times {10}^{- 2}

⇒x=81⇒ x = 81

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