Question

In a first order reaction what is the retio of t 15/16 : t 1/2 ?

Answer 1

Answer:

Explanation:30

Answer 2

Answer:

The ratio of $t_{15/16}$ : $t_{1/2}$ is 4:1.

Explanation:

For first order reaction,

ln $[A]$ = -kt + ln$[A]_0$ ...... (1)

where $[A]$ = concentration of the reactant and $[A]_0$ = initial concentration of the reactant.

Rewrite equation (1) as follows:

ln $[A]$ = -kt + ln$[A]_0$

ln $[A]_0$ - ln$[A]$ = kt

ln $\frac{[A]_0}{[A]}$ = kt ...... (2)

For $t=t_{15/16 }$,

$[A]=\frac{[A]_0}{16}$

Then from (2),

ln $\frac{[A]_0}{[A]_0/16}$ = $kt_{15/16}$

⇒ ln $16$ = $kt_{15/16}$

⇒ ln $2^4$ = $kt_{15/16}$

⇒ 4 ln $2$ = $kt_{15/16}$ ...... (3)

For $t=t_{1/2 }$,

$[A]=\frac{[A]_0}{2}$

Then from (2),

ln $\frac{[A]_0}{[A]_0/2}$ = $kt_{1/2}$

⇒ ln $2$ = $kt_{1/2}$ ...... (4)

Substitute the value of ln $2$ in equation (3) as follows:

⇒ 4 $kt_{1/2}$ = $kt_{15/16}$

⇒ 4 $t_{1/2}$ = $t_{15/16}$

⇒ $\frac{t_{15/16}}{t_{1/2}} = \frac{4}{1}$

Therefore, the ratio is 4:1.

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