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KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • question_answer
    The decompostion \[N{{H}_{3}}\] gas on a heated tungsten surface gave the following results:
    Initial pressure (mm) 65 105 y 185
    Half - life (sec) 290 X 670 820
    Calculate approximately the values of x and y.

    A) \[x=410\,\,\sec \]

    B) \[x=467\,\,\sec \]

    C) \[x=490\,\,\sec \]

    D) \[x=430\,\,\sec \]

    Correct Answer: B

    Solution :

    y = 115 mm y = 150  mm y = 120 mm y = 105 mm
    Initial pressure 65 105 Y 185
    Half life 290 X 670 820
    Initial pressure of gas \[\alpha \] Initial moles of gas in above question.
    Half life \[\alpha \] Initial pressure So, it must be zero order reaction
    \[{{t}_{1/2}}=\frac{{{C}_{O}}}{2k}=\frac{{{P}_{O}}}{2k}\]  \[290=\frac{65}{2\,k}\]     \[\Rightarrow \]\[k=\frac{65}{2\times 290}=0.112\,\,mm\] of Hg/sec
    \[x=\frac{105\times 2\times 290}{2\times 65}=468\,\,\sec \]
    \[670=\frac{y\times 2\times 290}{2\times 64}\]     \[\Rightarrow \]   y = 150 mm of Hg


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