JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Self Evaluation Test - Kinetic Theory

  • question_answer
    Two vessels separately contain two ideal gases A and B at the same temperature. The pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:

    A) \[\frac{3}{4}\]

    B) \[2~\]   

    C) \[\frac{1}{2}\]

    D) \[\frac{2}{3}\]

    Correct Answer: A

    Solution :

    [a] From \[\,PV=nRT\]  \[{{P}_{A}}=\frac{{{\rho }_{A}}{{M}_{A}}}{RT}\text{ and }{{P}_{B}}=\frac{{{\rho }_{B}}{{M}_{B}}}{RT}\]  From question, \[\frac{{{P}_{A}}}{{{P}_{B}}}=\frac{{{\rho }_{A}}}{{{\rho }_{B}}}\frac{M{{ & }_{A}}}{{{M}_{B}}}=2\frac{M{{ & }_{A}}}{{{M}_{B}}}=\frac{3}{2}\]  \[\text{So, }\frac{M{{ & }_{A}}}{{{M}_{B}}}=\frac{3}{4}\]


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