Question

The half-life period of a first order reaction is 1000 seconds. Its rate constant is:

• A. \(0.693 \, {sec}^{-1}\)
• B. \(6.93 \times 10^{-2} \, {sec}^{-1}\)
• C. \(6.93 \times 10^{-3} \, {sec}^{-1}\)
• D. \(6.93 \times 10^{-4} \, {sec}^{-1}\)
• E. \(6.93 \times 10^{-1} \, {sec}^{-1}\)

Hint:

For first-order reactions, the half-life is inversely proportional to the rate constant.

Answer 1

The Correct Option is D

For a first-order reaction, the relationship between half-life (\(t_{1/2}\)) and rate constant (\(k\)) is given by: \[ t_{1/2} = \frac{0.693}{k} \] Substituting the given half-life (\(1000 \, {sec}\)): \[ 1000 = \frac{0.693}{k} \] Solving for \(k\): \[ k = \frac{0.693}{1000} = 6.93 \times 10^{-4} \, {sec}^{-1} \]