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  • question_answer
    In a first order reaction \[A\xrightarrow[{}]{{}}B,\] if k is rate constant and  initial  concentration  of the reactant A is 0.5 M then the half-life is :                                                               [AIPMT (S) 2007]

    A)                             \[\frac{0.693}{0.5\,k}\]

    B) \[\frac{\log \,2}{k}\]

    C)       \[\frac{\log \,2}{k\sqrt{0.5}}\]

    D)       \[\frac{\ln \,2}{k}\]

    Correct Answer: D

    Solution :

    [d] For first order reaction
                \[k=\frac{2.303}{t}\log \frac{a}{(a-x)}\]
                \[{{t}_{1/2}}=\frac{2.303}{k}\log \frac{a}{a-\frac{a}{2}}\]
                \[=\frac{2.303}{k}\log \,2\]
    \[or\frac{\ln \,2}{k}\]


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