The rate of a first-order reaction is 0.04mol l ^ - 1 s ^ - 1 at 10 second and 0.03mol l ^ - 1 s ^ - 1 at 20 seconds after initiation of the reaction. The half-life period of the reaction is:

Correct answer: A. 24 . 1s cases Rate & Time 0.04 & 10 0.03 & 20 cases For first order reaction r ∝ conc. r _ 1 r _ 2 = C _ 1 C _ 2 = (4)/(3) ∴ k = 2.303 t _ 2 - t _ 1 log C _ 1 C _ 2 ⇒ 0.693 t _ 1/2 = (2.303)/(20 - 10)log (4)/(3) On solving t _ 1/2 = 24.1s

NEET 2016

Exam: NEET
Year: 2016
Subject: Chemistry
Chapter: Chemical Kinetics

NEET 2016 · Chemistry · Chemical Kinetics

The rate of a first-order reaction is 0.04mol l ^ - 1 s ^ - 1 at 10...

The rate of a first-order reaction is

0.04mol{l}^{- 1}{s}^{- 1}

10

second and

0.03mol{l}^{- 1}{s}^{- 1}

20

seconds after initiation of the reaction. The half-life period of the reaction is:

Options

A $24 . 1s$
B $34 . 1s$
C $44 . 1s$
D $54 . 1s$

Correct answer

A. $24 . 1s$

Step-by-step solution

\begin{cases}Rate & Time \\ 0.04 & 10 \\ 0.03 & 20\end{cases}

For first order reaction r

∝

conc.

\dfrac{{r}_{1}}{{r}_{2}} = \dfrac{{C}_{1}}{{C}_{2}} = \dfrac{4}{3}

∴ k = \dfrac{2.303}{{t}_{2} - {t}_{1}}log \dfrac{{C}_{1}}{{C}_{2}}

⇒ \dfrac{0.693}{{t}_{1/2}} = \dfrac{2.303}{20 - 10}log \dfrac{4}{3}

On solving

{t}_{1/2} = 24.1s

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