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KVPY Sample Paper KVPY Stream-SX Model Paper-13

  • question_answer
    0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume \[10\,{{\text{m}}^{3}}\] at 1000 K, given R is the gas constant in \[\text{J}{{\text{K}}^{-1}}\]\[\text{mo}{{\text{l}}^{-1}}\]m, x is:

    A) \[\frac{2\text{R}}{4+12}\]

    B) \[\frac{2\text{R}}{4-\text{R}}\]

    C) \[\frac{4-\text{R}}{2\text{R}}\]

    D) \[\frac{4+\text{R}}{2\text{R}}\]

    Correct Answer: C

    Solution :

    \[{{n}_{T}}\,=\,(0.5+x)\]
    \[\text{PV}\,=n\,\times \,\text{R}\times \text{T}\]
    \[200\times 10\,=\,(0.5+x)\,\times \,\text{R}\,\times \,1000\]
    \[2\,=\,(0.5+x)\text{R}\]
    \[\frac{2}{\text{R}}\,=\,\frac{1}{2}+\,x\]
    \[\frac{\text{4}}{\text{R}}\,-\,1\,=\,2x\]\[\Rightarrow \] \[\frac{4-\text{R}}{2\text{R}}\,=\,x.\]


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