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Stuck here, help me understand: In a first order reaction, the concentration of the reactant, decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is

In a first order reaction, the concentration of the reactant, decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is

  • Option 1)

    30 minutes

  • Option 2)

    15 minutes

  • Option 3)

    7.5 minutes

  • Option 4)

    60 minutes.

 
Answers (1)
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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{2.303}{15}log\frac{0.8}{0.4}

k=\frac{0.693}{15}

for next condition

k=\frac{0.693}{15}=\frac{2.303}{t}log\frac{0.1}{0.025}

t=30 min


Option 1)

30 minutes

Correct option

Option 2)

15 minutes

Incorrect option

Option 3)

7.5 minutes

Incorrect option

Option 4)

60 minutes.

Incorrect option

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