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JEE Main 201815 AprilMorning ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Morning Shift
Mode
Online
Subject
Chemistry
Chapter
Chemical Kinetics

JEE Main 2018 · 15 April · Morning Shift · Online · Chemistry · Chemical Kinetics

N_2 O_5 decomposes to NO_2 and O_2 and follows first order...

N2O5\mathrm{N}_2 \mathrm{O}_5 decomposes to NO2\mathrm{NO}_2 and O2\mathrm{O}_2 and follows first order kinetics. After 5050 minutes, the pressure inside the vessel increases from 50 mm Hg50 \mathrm{~mm} \mathrm{~Hg} to 87.5 mm Hg87.5 \mathrm{~mm} \mathrm{~Hg}. The pressure of the gaseous mixture after 100100 minutes at constant temperature will be ______.

Options

  1. A136.25 mm Hg136.25 \mathrm{~mm} \mathrm{~Hg}
  2. B106.25 mm Hg106.25 \mathrm{~mm} \mathrm{~Hg}
  3. C175.0 mm Hg175.0 \mathrm{~mm~Hg}
  4. D116.25 mm Hg116.25 \mathrm{~mm} \mathrm{~Hg}

Correct answer

B. 106.25 mm Hg106.25 \mathrm{~mm} \mathrm{~Hg}

Step-by-step solution

N2O5→2NO2+12O2\mathrm{N}_2 \mathrm{O}_5 \rightarrow 2 \mathrm{NO}_2+\frac{1}{2} \mathrm{O}_2  At t=05000 At t=50 min50−p12p1p12\begin{array}{llll}\text{ At } \mathrm{t}=0 & 50 & 0 & 0 \\ \text{ At } \mathrm{t}=50 \mathrm{~min} & 50-\mathrm{p}_1 & 2 \mathrm{p}_1 & \frac{\mathrm{p}_1}{2}\end{array} Total pressure at 5050 minutes =50−p1+2p1+p12=87.550+3p12=87.53p12=37.5∴p1=37.5×23=25\begin{aligned} &=50-\mathrm{p}_1+2 \mathrm{p}_1+\frac{\mathrm{p}_1}{2}=87.5 \\ &50+\frac{3 \mathrm{p}_1}{2}=87.5 \\ &\frac{3 \mathrm{p}_1}{2}=37.5 \\ &\therefore \quad \mathrm{p}_1=\frac{37.5 \times 2}{3}=25 \end{aligned} At t=100 min50−p22p2p22\mathrm{t}=100 \mathrm{~min} \quad 50-\mathrm{p}_2 \quad 2 \mathrm{p}_2 \quad \frac{\mathrm{p}_2}{2} 5050 minutes is half life period For 100100 minutes i.e. for 22 half lives 50−p2=12.550-p_2=12.5 ∴p2=37.5 mm of Hg\therefore \mathrm{p}_2=37.5 \mathrm{~mm} \text{ of } \mathrm{Hg} Total pressure at 100100 minutes =50−p2+2p2+p22=50-\mathrm{p}_2+2 \mathrm{p}_2+\frac{\mathrm{p}_2}{2} =50+3p22=50+32×37.5=50+\frac{3 \mathrm{p}_2}{2}=50+\frac{3}{2} \times 37.5 =50+56.25=50+56.25 =106.25 mm=106.25 \mathrm{~mm} of Hg\mathrm{Hg}
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