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NEET AIPMT SOLVED PAPER SCREENING 2012

  • question_answer
    \[{{\text{p}}_{\text{A}}}\]and \[{{\text{p}}_{\text{B}}}\]are the vapour pressure of pure liquid components, A and B, respectively of an ideal binary solution. If \[{{\text{x}}_{\text{A}}}\] represents the mole fraction of component A, the total pressure of the solution will be

    A) \[{{p}_{A}}+{{x}_{A}}({{p}_{B}}-{{p}_{A}})\]       

    B) \[{{p}_{A}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\]

    C) \[{{p}_{B}}+{{x}_{A}}({{p}_{B}}-{{p}_{A}})\]        

    D) \[{{p}_{B}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\]

    Correct Answer: D

    Solution :

    Total pressure,\[{{p}_{T}}=p{{'}_{A}}+p{{'}_{B}}\]                             ...(i) We know that, \[p{{'}_{A}}={{p}_{A}}{{x}_{A}}\]                                 \[p{{'}_{B}}={{p}_{B}}{{x}_{B}}\] Substituting the values of \[p{{'}_{A}}\]and \[p{{'}_{B}}\] in Eq. (i)                 \[{{p}_{T}}={{p}_{A}}{{x}_{A}}+{{p}_{B}}{{x}_{B}}\] \[[{{x}_{A}}+{{x}_{B}}=1\Rightarrow {{x}_{A}}=1-{{x}_{B}}or\,{{x}_{B}}=1-{{x}_{A}}]\]                 \[={{p}_{A}}{{x}_{A}}+{{p}_{B}}(1-{{x}_{A}})\]                 \[={{p}_{A}}{{x}_{A}}+{{p}_{B}}-{{p}_{B}}{{x}_{A}}\] \[\therefore \]  \[{{p}_{T}}x{{p}_{B}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\]


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