A first order reaction is 50% completed in 1.26\times 10^{14}s. How much time would it take for 100% completion?

  • Option 1)

    1.26\times 10^{15}s

  • Option 2)

    2.25\times 10^{14}s

  • Option 3)

    2.25\times 10^{28}s

  • Option 4)

    Infinite

 

Answers (1)

As we learned in concept

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}

 

 

  

 

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}

 

 

 In a first order reaction, R\rightarrow P

Rate = k[R], k= constant

\ln \left ( \frac{a}{a-x} \right )= kt

Given that  at x= a/2, t= 1.26*10^{14}

but for 100% completion, x=a and that would render equation 1 as undefined.

So,first order reactions take infinite time to complete.


Option 1)

1.26\times 10^{15}s

Incorrect option

Option 2)

2.25\times 10^{14}s

Incorrect option

Option 3)

2.25\times 10^{28}s

Incorrect option

Option 4)

Infinite

Correct option

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