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NEET Sample Paper NEET Sample Test Paper-72

  • question_answer
    For two gases of molecular weights\[{{M}_{A}}\,\,and\,\,{{M}_{B}}\], at temperature\[{{T}_{A}}\,\,and\,\,{{T}_{B}}\],\[{{T}_{A}}{{M}_{B}}={{T}_{B}}{{M}_{A}}\], then which property has the same magnitude for both the gases.

    A) density             

    B) pressure

    C) KE per mol                    

    D) \[{{V}_{rms}}\]

    Correct Answer: D

    Solution :

    (i) Density of a gas \[\left( \rho  \right) = \frac{PM}{RT}\] Since \[\frac{{{M}_{B}}}{{{T}_{B}}}=\frac{{{M}_{A}}}{{{T}_{A}}}\], \[\therefore \] at the same pressure \[={{\rho }_{A}}={{\rho }_{B}}.\] But if pressure is different, then \[{{\rho }_{A}}\ne {{\rho }_{B}}.\] (ii) Pressure of the gases would be equal if their densities are equal otherwise not.            (iii) \[\operatorname{KE}\,\,per\,\,mol\,\,=\,\,\frac{3}{2}RT\] \[\therefore \] It will be different for the two gases. (iv) \[{{V}_{rms}}=\sqrt{\frac{3RT}{M}},\] since \[\frac{{{T}_{A}}}{{{M}_{A}}}=\frac{{{T}_{B}}}{{{M}_{B}}}\]; \[{{V}_{rms}}\] of \[A={{V}_{rms}}\,\,of\,\,B\]


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