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MGIMS WARDHA MGIMS WARDHA Solved Paper-2014

  • question_answer
    An evacuated glass vessel weighs 50 g when empty, 144.0 g when filled with a liquid of density\[0.47\text{ }g\text{ }m{{L}^{-1}}\]and 50.5 g when filled with an ideal gas at 760 mm Hg and 300 K. The molar mass of the ideal gas is \[[R=0.0821L\text{ }atm\text{ }{{K}^{-1}}mo{{l}^{-1}}]\]

    A)  61.575                 

    B)  130.98

    C)  123.75                 

    D)  47.87

    Correct Answer: A

    Solution :

                    Weight of empty glass vessel \[=50\text{ }g\] Weight of glass vessel filled with liquid = 144.0 g \[\therefore \] Weight of liquid \[=144-50=94g\] Density of liquid\[=0.47\text{ }gm{{L}^{-1}}\] \[\therefore \]Volume of liquid\[=\frac{94}{0.47}=200\text{ }mL=0.2\text{ }L\] Mass of glass vessel filled with gas \[=50.5\text{ }g\] \[\therefore \] Mass of gas (m) \[=50.5-50=0.5\text{ }g\] By using ideal gas equation. \[pV=\frac{m}{M}RT\] Where,                 \[p=760\text{ }mm.\text{ }Hg=1\text{ }atm,\] \[V=0.2L,T=300K.\] and                        \[R=0.0821\text{ }L\text{ }atm\text{ }{{K}^{-1}}mo{{l}^{-1}}\] \[\therefore \]Molar mass\[(M)=\frac{mRT}{pV}\]                                 \[=\frac{0.5\times 0.0821\times 300}{1\times 0.2}\] \[=61.575\text{ }g\text{ }mo{{l}^{-1}}\]


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