Sankalp NEET Full Test-5 Question-65 Solution

Question: 65: The half life of a first order reaction is 2000 years. If the concentration after 8000 years is 0.02 M , then the initial concentration was :

(1) 0.16 M

(2) 0.32 M

(3) 0.08 M

(4) 0.04 M

Answer: Option (2)

Explanation:

For a first order reaction, the concentration decreases by half after every half-life.

Given half-life is 2000 years and time elapsed is 8000 years.

Number of half-lives elapsed is:

\frac{8000}{2000} = 4

After one half-life, concentration becomes half of the initial concentration.

After four half-lives, the concentration becomes:

\frac{a}{2^4} = \frac{a}{16}

Given concentration after 8000 years is:

\frac{a}{16} = 0.02

Solving for initial concentration a:

a = 0.02 \times 16 = 0.32

Therefore, the initial concentration was 0.32 M.

Hence, option (2) is correct.