Question

If the rate constant for a first order reaction is k the time (t) required for the completion of 99% of the reaction is given by:

• A. t=0.693/k
• B. t=6.909/k
• C. t=4.606/k
• D. t=2.303/k

Answer 1

The Correct Option is C

To find the time required for the completion of 99% of a first-order reaction, we use the relation: \(k = \frac{1}{t}\ln\left(\frac{[A]_0}{[A]}\right)\)

where \(k\) is the rate constant, \(t\) is time, \([A]_0\) is initial concentration, and \([A]\) is concentration at time \(t\).

For 99% completion: \(\frac{[A]}{[A]_0} = 0.01\)

Substituting: \(k = \frac{1}{t}\ln\left(\frac{[A]_0}{0.01[A]_0}\right)\)

Canceling \([A]_0\): \(k = \frac{1}{t}\ln(100)\)

Using \(\ln(100) = 4.606\): \(k = \frac{4.606}{t}\)

Thus, \(t = \frac{4.606}{k}\)

Final Answer: \(t = \frac{4.606}{k}\)