Question

A first order reaction take \(30\) minutes for \(75\%\) decomposition, calculate its rate constant ?

• A. \(0.0238 \text{minute}^{-1}\)
• B. \(0.0463 \text{minute}^{-1}\)
• C. \(0.0715 \text{minute}^{-1}\)
• D. \(0.0957 \text{minute}^{-1}\)

Hint:

Use k = (2.303/t) log (a/(a - x)); 75% decomposition leaves 25 percent.

Answer 1

The Correct Option is B

Step 1: Half-Life Shortcut:
75% decomposition takes exactly two half-lives, because 100 to 50 to 25.

Step 2: Compute:
So $2\,t_{1/2} = 30$ min and $t_{1/2} = 15$ min. Then $k = 0.693/15 = 0.0462\ \text{min}^{-1}$.

Step 3: Match:
This is the value 0.0463 given in option (B).

Final Answer:
Option (B). \[ \boxed{\text{(B) } 0.0463\ \text{min}^{-1}} \]