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

  • question_answer
    The density of a gas at \[{{27}^{o}}C\] and 1 atm is d. Pressure remaining constant at which of the following temperatures will its density become 0.75 d     [CBSE PMT 1992]

    A)                 \[{{20}^{o}}C\] 

    B)                 \[{{30}^{o}}C\]

    C)                 400 K    

    D)                 300 K

    Correct Answer: C

    Solution :

               At constant pressure            \[V\propto nT\propto \frac{m}{M}T\]            \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{{{m}_{1}}{{T}_{1}}}{{{m}_{2}}{{T}_{2}}}\therefore \frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{V}_{1}}}{{{m}_{1}}}\times \frac{{{m}_{2}}}{{{V}_{2}}}=\frac{{{d}_{2}}}{{{d}_{1}}}\]\[\Rightarrow \frac{{{300}^{o}}K}{{{T}_{2}}}=\frac{0.75d}{d}\]                 \[{{T}_{2}}=\frac{300}{0.75}={{400}^{o}}K\]

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