Question

If the half life of a first order reaction is \(6.93 \text{ minutes}\) then the time required for completion of \(99 %\) of the reaction will be ____ minutes.
(Given : \(\log 2 = 0.3010\))}

Answer 1

Correct Answer: 46

Step 1: Understanding the Question:
We need to find the time required for a first-order reaction to reach \(99%\) completion given its half-life.
Step 2: Key Formula or Approach:
1. Rate constant \(k = \frac{0.693}{t_{1/2}}\).
2. Time \(t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}\).
Step 3: Detailed Explanation:
1. Calculate the rate constant (\(k\)):
\[ k = \frac{0.693}{6.93} = 0.1 \text{ min}^{-1} \]
2. Calculate the time for \(99%\) completion (\(t_{99%}\)):
If \(99%\) is completed, the remaining reactant is \(1%\) of initial.
\([A]_0 = 100\), \([A]_t = 1\).
\[ t = \frac{2.303}{0.1} \log \frac{100}{1} \]
\[ t = 23.03 \times \log(10^2) \]
\[ t = 23.03 \times 2 = 46.06 \text{ minutes} \]
Rounding to the nearest integer, we get 46 minutes.
Step 4: Final Answer:
The time required is 46 minutes.