A) \[{{t}_{1/2}}\propto {{R}_{0}}\]
B) \[{{t}_{1/2}}\propto 1\text{/}{{R}_{0}}\]
C) \[{{t}_{1/2}}\propto R_{0}^{2}\]
D) \[{{t}_{1/2}}\propto 1/R_{0}^{2}\]
Correct Answer: A
Solution :
For a zero order reaction rate \[\frac{-d\,[R]}{dt}=k\] Integrating both sides w.r.t. t, we get \[\left[ R \right]=-kt+\left[ C \right]\] At time \[t=0,\]\[[R]=[{{R}_{0}}]\] \[\therefore \] \[[R]=-kt+[{{R}_{0}}]\] When \[t={{t}_{1/2}},\]\[[R]=\frac{[{{R}_{0}}]}{2}\] \[\therefore \]\[\frac{[{{R}_{0}}]}{2}-[{{R}_{0}}]=-k{{t}_{1/2}}\] \[{{t}_{1/2}}=\frac{[{{R}_{0}}]}{2k}\] \[\Rightarrow \] \[{{t}_{1/2}}\propto [{{R}_{0}}]\]
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