Q28 / 150 · MHT CET 2026 (13 April Shift 2) · Chemistry
A first order reaction takes $16$ minutes for it's $50\%$ completion. What fraction that would react in $32$ minutes from the beginning?
- A$1/2$
- B$1/4$
- C$1/8$
- Correct answerD$3/4$
Solution
For a first order reaction, the half-life is given as $t_{1/2} = 16$ minutes.
The time given is $t = 32$ minutes.
The number of half-lives is $n = \dfrac{t}{t_{1/2}} = \dfrac{32}{16} = 2$.
The fraction of the reactant remaining after $n$ half-lives is $\dfrac{1}{2^n}$.
Fraction remaining $= \dfrac{1}{2^2} = \dfrac{1}{4}$.
The fraction of the reactant that has reacted is $1 - \dfrac{1}{4} = \dfrac{3}{4}$.
Answer: $3/4$
The time given is $t = 32$ minutes.
The number of half-lives is $n = \dfrac{t}{t_{1/2}} = \dfrac{32}{16} = 2$.
The fraction of the reactant remaining after $n$ half-lives is $\dfrac{1}{2^n}$.
Fraction remaining $= \dfrac{1}{2^2} = \dfrac{1}{4}$.
The fraction of the reactant that has reacted is $1 - \dfrac{1}{4} = \dfrac{3}{4}$.
Answer: $3/4$
Hence, the correct answer is option: 'D'.