# The rate of first order reaction is 0.04 mol l-1 s-1 at 10 seconds and 0.03 mol l-1 s-1 at 20 seconds after intiation of the reaction. The half - life period of the reaction is : Option 1) 24.1 s Option 2) 34.1 s Option 3) 44.1s Option 4) 54.1 s

Arrhenius Equation -

Arrhenius gave the quantitative dependence of rate constant on temperature by the Arrhenius equation.

- wherein

$k = A e^{-E_{a}/RT}$

$In k=InA-\frac{E_{a}}{RT}$

$k$ = Rate constant

For a first-order reaction

$K=\frac{2.303}{t_{2}-t_{1}}. \log\frac{[A]_{1}}{[A]_{2}}$

$\therefore K=\frac{2.303}{20-10}. \log\frac{(0.04)}{(0.03)}=0.0287 sec^{-1}$

$t_{\frac{1}{2}}=\frac{0.693}{K}= \frac{(0.693)}{(.0287)}=24.1 sec$

Option 1)

24.1 s

This option is correct.

Option 2)

34.1 s

This option is incorrect.

Option 3)

44.1s

This option is incorrect.

Option 4)

54.1 s

This option is incorrect.

### Preparation Products

##### Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
##### Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
##### Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
##### Test Series NEET May 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-