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JIPMER 2012
Exam
JIPMER
Year
2012
Subject
Chemistry
Chapter
Chemical Kinetics

JIPMER 2012 · Chemistry · Chemical Kinetics

For a zero order reaction

For a zero order reaction

Options

  1. At1/2∝R0t_{1/2} \propto R_0
  2. Bt1/2∝1/R0t_{1/2} \propto 1 / R_0
  3. Ct1/2∝R02t_{1/2} \propto R_0^2
  4. Dt1/2∝1/R02t_{1/2} \propto 1 / R_0^2

Correct answer

A. t1/2∝R0t_{1/2} \propto R_0

Step-by-step solution

For a zero order reaction rate, −d[R]dt=k-\frac{d[R]}{d t}=k On integrating, we get [R]=−kt+[C][R]=-k t+[C] When t=0,[R]=[R0]t=0,[R]=\left[R_0\right] ∴[C]=[R0]\therefore \quad[C]=\left[R_0\right] ∴[R]=−kt+[R0]\therefore \quad[R]=-k t+\left[R_0\right] When, t=t1/2,[R]=[R0]2t=t_{1/2},[R]=\frac{\left[R_0\right]}{2} ∴[R0]2−[R0]=−kt1/2\therefore \quad \frac{\left[R_0\right]}{2}-\left[R_0\right]=-k t_{1/2} ∴t1/2=[R0]2k\therefore \quad t_{1/2}=\frac{\left[R_0\right]}{2 k} $t_{1/2} \propto\left[R_0\right]
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