Verified Solution • 2025–26 Session moderate

QJEEM10Ch24fe: JEE Main 2010 Chemistry - Class 12 JEEM10Ch24fe Solution: The time for half life period of a certain reaction A products…

The time for half life period of a certain reaction A →\to products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its concentration to come from 0.50 to 0.25 mol L–1 if it is a zero order reaction ?

Multiple Choice Options

  • A 4 h
  • B 0.5 h
  • C 0.25 h
  • D 1 h

Step-by-Step Verified Solution

For the reaction

A  →  A\,\, \to \,\, Product ; given t1/2=1  {t_{1/2}} = 1\,\, hour

for a zero order reaction

tcompletion  =[A0]k=initial  conc.rate  constan⁡t{t_{completion}}\,\, = {{\left[ {{A_0}} \right]} \over k} = {{initial\,\,conc.} \over {rate\,\,cons\tan t}}

∴\therefore      t1/2=[A0]2K\,\,\,\,\,{t_{1/2}} = {{\left[ {{A_0}} \right]} \over {2K}}

or      k=[A0]2t1/2=22×1=1  mol lit−1 hr−1\,\,\,\,\,k = {{\left[ {{A_0}} \right]} \over {2{t_{1/2}}}} = {2 \over {2 \times 1}} = 1\,\,mol\,li{t^{ - 1}}\,h{r^{ - 1}}

Further for a zero order reaction

k=dxdt=change   in   concentrationtimek = {{dx} \over {dt}} = {{change\,\,\,in\,\,\,concentration} \over {time}}

I=0.50−0.25time   I = {{0.50 - 0.25} \over {time}}\,\,\,

∴\therefore      \,\,\,\,\, time =0.25  hr.= 0.25\,\,hr.

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