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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.

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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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