Question

In first order reaction 20 millimole of reactant is reduced to 10 millimole in \(1\cdot 151\) minute. Find rate constant.

• A. \(0\cdot 6023\text{ minute}^{-1}\)
• B. \(6\cdot 120\text{ minute}^{-1}\)
• C. \(0\cdot 3010\text{ minute}^{-1}\)
• D. \(2\cdot 010\text{ minute}^{-1}\)

Hint:

Time taken for 50 percent change is the half-life, and k = 0.693 / t half.

Answer 1

The Correct Option is A

Step 1: Use the integrated rate law:
$k = \frac{2.303}{t}\log\frac{[A]_0}{[A]}$.

Step 2: Substitute:
\[ k = \frac{2.303}{1.151}\log\frac{20}{10} = 2.001\times 0.3010 = 0.6023\text{ min}^{-1} \]
This is option (A).

Final Answer:
$k = 0.6023$ per minute. \[ \boxed{0.6023\text{ min}^{-1}} \]