The rate of first order reaction is 0.04 mol l-1 s-1 at 10 seconds and 0.03 mol l-1 s-1 at 20 seconds after intiation of the reaction. The half - life period of the reaction is :

  • Option 1)

    24.1 s

  • Option 2)

    34.1 s

  • Option 3)

    44.1s

  • Option 4)

    54.1 s

 

Answers (1)

 

Arrhenius Equation -

Arrhenius gave the quantitative dependence of rate constant on temperature by the Arrhenius equation.

- wherein

k = A e^{-E_{a}/RT}

In k=InA-\frac{E_{a}}{RT}

k = Rate constant

 

 For a first-order reaction

K=\frac{2.303}{t_{2}-t_{1}}. \log\frac{[A]_{1}}{[A]_{2}}

\therefore K=\frac{2.303}{20-10}. \log\frac{(0.04)}{(0.03)}=0.0287 sec^{-1}

t_{\frac{1}{2}}=\frac{0.693}{K}= \frac{(0.693)}{(.0287)}=24.1 sec

 


Option 1)

24.1 s

This option is correct.

Option 2)

34.1 s

This option is incorrect.

Option 3)

44.1s

This option is incorrect.

Option 4)

54.1 s

This option is incorrect.

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