JEE Main & Advanced Chemistry States of Matter Question Bank Ideal gas equation and Related gas laws

  • question_answer X ml of \[{{H}_{2}}\] gas effuses through a hole in a container in 5 seconds. The time taken for the effusion of the same volume of the gas specified below under identical condition is [IIT 1996]

    A)                 10 seconds : He

    B)                 20 seconds : \[{{O}_{2}}\]

    C)                 25 seconds : CO

    D)                 55 seconds : \[C{{O}_{2}}\]

    Correct Answer: B

    Solution :

               \[r\propto \frac{1}{\sqrt{M}}\]      \[\because \,\,r=\frac{Volume\,\,effused}{time\,\,taken}=\frac{V}{t}\]                    \[\frac{V}{t}\propto \frac{1}{\sqrt{M}}\] \for same volumes (V constant)                    \[t\propto \sqrt{M}\,\therefore \frac{{{t}_{1}}}{{{t}_{2}}}=\sqrt{\frac{{{M}_{1}}}{{{M}_{2}}}}\]                    \[{{t}_{He}}={{t}_{{{H}_{2}}}}\sqrt{\frac{{{M}_{He}}}{{{M}_{{{H}_{2}}}}}}=5\sqrt[{}]{\frac{4}{2}}=5\sqrt{2}s.\]                    \[{{t}_{{{O}_{2}}}}=t\]\[=5\sqrt[{}]{\frac{32}{2}}=20s\]                                 \[{{t}_{CO}}=\]\[5\sqrt[{}]{\frac{28}{2}}=5\sqrt{14}s\] ;  \[{{t}_{C{{O}_{2}}}}=\]\[5\sqrt[{}]{\frac{44}{2}}=5\sqrt{22}s\]

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