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The half -life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be \left ( \log 2= 0.301 \right )

  • Option 1)

    230.3 minutes

  • Option 2)

    23.03 minutes

  • Option 3)

    46.06 minutes

  • Option 4)

    460.6 minutes

 

Answers (1)

best_answer

As we learnt in

First Order Reaction -

The rate of the reaction is proportional to the first power of the concentration of the reaction

- wherein

Formula:

R    \rightarrow        P

a                 0

a-x             x

rate[r]=K[R]^{1}

\frac{-d(a-x)}{dt}=K(a-x)

\frac{-dx}{dt}=K(a-x)  [differentiate rate law]

ln \:[\frac{a}{a-x}]=kt \:(Integrated rate law)

Unit of k=sec^{-1}

t_\frac{1}{2}=\frac{0.693}{k}

 

 

 K=\frac{0.693}{t\frac{1}{2}}=\frac{0.693}{6.93}=\frac{1}{10}

t=\frac{2.303}{K}\:log\frac{100}{1}

t=\frac{2.303}{\frac{1}{10}}\:log10^{2}

t=46.06


Option 1)

230.3 minutes

Incorrect option

Option 2)

23.03 minutes

Incorrect option

Option 3)

46.06 minutes

Correct option

Option 4)

460.6 minutes

Incorrect option

Posted by

divya.saini

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