### NEET Solved Paper 2016 Question 4

##### Question: The rat e of a first -order react ion is $ 0\text{.04}\ mol\ {{\ell }^{-1}}{s^{-1}} $ at 10 seconds and $ 0.03\ \text{mol }{{\ell }^{-1}}{s^{-1}} $ at 20 seconds after initiation of the reaction. The half-life period of the reaction is:

#### Options:

A) 24.1 s

B) 34.1 s

C) 44.1 s

D) 54.1 s

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

- $ K=\frac{2.303}{(t _2-t _1)}\log ( \frac{a-x _1}{a-x _2} ) $ $ K=\frac{2.303}{(20-10)}\log ( \frac{0.04}{0.03} ) $ $ K=\frac{2.303\times 0.1249}{10} $ $ \frac{2.303\times \log 2}{{{t} _{1/2}}}=\frac{2.303\times .1249}{10} $ $ {{t} _{1/2}}=\frac{0.3010\times 10}{0.1249}=24.1,\sec $