Question

For the first order reaction, 80 % of the reactant decomposes in 60 minutes. Calculate the half life of the reaction.

• A. 40 min
• B. 26 min
• C. 35 min
• D. 20 min

Hint:

Find k from 20 percent remaining after 60 minutes, then use t half = 0.693 / k.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For a first order reaction, \(k=\dfrac{2.303}{t}\log\dfrac{a}{a-x}\).

Step 2: Find k
80% decomposed leaves 20%, so \(\dfrac{a}{a-x}=5\).
\(k=\dfrac{2.303}{60}\log 5=\dfrac{2.303\times 0.699}{60}=0.0268\ \text{min}^{-1}\).

Step 3: Half life
\(t_{1/2}=\dfrac{0.693}{0.0268}\approx 26\) min.

Final Answer:
The half life of the reaction is about 26 minutes. \[ \boxed{\text{(B) }26\ \text{min}} \]