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KVPY Sample Paper KVPY Stream-SX Model Paper-7

  • question_answer
    Reaction \[A+B\to C+D\] follows rate law, \[r=k{{[A]}^{1/2}}{{[B]}^{1/2}}\] starting with 1 M of A and B each. What is the time taken for concentration of A become 0.1 M? Give \[k=2.303\times {{10}^{-2}}{{\sec }^{-1}}\].

    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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