JEE Main & Advanced Chemistry Chemical Kinetics / रासायनिक बलगतिकी Sample Paper Topic Test - Chemical Kinetics

  • question_answer
    In a reaction involving one single reactant, the fraction of the reactant consumed may be defined as \[f=\left[ 1-\left( C/{{C}_{0}} \right) \right],\] where \[{{C}_{0}}\] and C are the concentrations of the reactant at the start and after time t. For a first-order reaction:

    A) \[\frac{df}{dt}=k\left( 1-f \right)\]

    B) \[-\frac{df}{dt}=kf\]

    C) \[-\frac{df}{dt}=k\left( 1-f \right)\]           

    D) \[\frac{df}{dt}=kf\]

    Correct Answer: A

    Solution :

    Given \[f=\left( 1-\frac{c}{{{c}^{o}}} \right),\] then \[\frac{c}{{{c}^{o}}}=\left( 1-f \right)\]
    \[\frac{df}{dt}=\frac{1}{{{c}^{o}}}\frac{dc}{dt}\] for first-order reaction
    \[-\frac{dc}{dt}=K\left[ c \right]\]
    \[\frac{df}{dt}=\frac{1}{{{c}^{o}}}K\left[ c \right]\] then \[\frac{df}{dt}=K\left( 1-f \right)\]

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