A) 10 sec
B) 100 sec
C) 1000 sec
D) 434 sec
Correct Answer: B
Solution :
\[A~~~~~~~+~~~~~~B~~~~~~~\to ~~~~~~~C~~~~~~~+~~~~~~~D\] \[t=0\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,0\] |
\[t=t\,\,\,\,\,\,\,\,\,\,\,\,1-x\,\,\,\,\,\,1-x\,\,\,\,\,\,x\,\,\,\,x\,\,\] |
\[r=k{{[A]}^{1/2}}{{[B]}^{1/2}}\] |
\[\Rightarrow \frac{dx}{dt}=k{{(1-x)}^{1/2}}{{(1-x)}^{1/2}}.\] or \[\frac{dx}{dt}=k(1-x).\] |
\[\Rightarrow t=\frac{1}{k}In\left( \frac{1}{1-x} \right)\,\,;\,\,\,\,\,t=\frac{2.303}{2.303\times {{10}^{-2}}}\,\,;\,\,\,\log \left( \frac{1}{0.1} \right)=100\,\,\sec .\] |
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