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

  • question_answer At constant volume and temperature conditions, the rate of diffusion \[{{D}_{A}}\] and \[{{D}_{B}}\] of gases A and B having densities \[{{\rho }_{A}}\] and \[{{\rho }_{B}}\] are related by the expression      [IIT 1993]

    A)                 \[{{D}_{A}}={{\left[ {{D}_{B}}\cdot \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right]}^{1/2}}\]    

    B)                 \[{{D}_{A}}={{\left[ {{D}_{B}}\cdot \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right]}^{1/2}}\]

    C)                 \[{{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right)}^{1/2}}\]

    D)                 \[{{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right)}^{1/2}}\]

    Correct Answer: D

    Solution :

                    \[\frac{{{D}_{A}}}{{{D}_{B}}}=\sqrt{\frac{{{\rho }_{B}}}{{{\rho }_{A}}}}={{\left[ \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right]}^{\frac{1}{2}}}\];  \[\therefore {{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right)}^{\frac{1}{2}}}\]


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