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CET Karnataka Medical CET - Karnataka Medical Solved Paper-2014

  • question_answer
    \[{{A}_{(g)}}\xrightarrow{\Delta }{{P}_{(g)}}+{{Q}_{(g)}}+{{R}_{(g)}}\], follows first order kinetics with a half-life of \[69.3s\]at\[{{500}^{o}}C\]. Starting from the gas A enclosed in a container at \[{{500}^{o}}C\] and at a pressure of\[0.4atm\], the total pressure of the system after \[230s\]will be

    A)  \[1.15atm\]       

    B)  \[1.32atm\]

    C)  \[1.22atm\] 

    D)  \[1.12atm\]

    Correct Answer: D

    Solution :

    : \[{{t}_{1/2}}=69.3s,\,\,t=230s,\,\,a=0.4atm\] For first order reaction, \[k=\frac{0.693}{{{t}_{1/2}}}=\frac{0.693}{69.3}=0.01{{s}^{-1}}\] \[k=\frac{2.303}{t}\log \frac{a}{a-x}=\frac{2.303}{230}\log \frac{0.4}{0.4-x}\] \[0.01=\frac{2.303}{230}\log \frac{0.4}{0.4-x}=0.01\log \frac{0.4}{0.4-x}\] \[\frac{0.01}{0.01}=\log \frac{0.4}{0.4-x}\] \[\Rightarrow \] \[10=\frac{0.4}{0.4-x}\]   \[x=0.36\] For the given reaction, \[\begin{matrix}    {} & {{A}_{(g)}}\xrightarrow{\Delta } & {{P}_{(g)}} & {{Q}_{(g)}} & {{R}_{(g)}}  \\    Initial & 0.4 & 0 & 0 & 0  \\    Final & 0.4-0.36 & 0.36 & 0.36 & 0.36  \\ \end{matrix}\] Total pressure \[=(0.4-0.36)+(3\times 0.36)=1.12\text{ }atm\]


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