Question

For a first-order reaction, the time required to reduce the concentration of the reactant to half its initial value is:

• A. \( \frac{0.3010}{k} \)
• B. \( \frac{1}{k} \)
• C. \( \frac{0.693}{k} \)
• D. \( \frac{2.303}{k} \)

Hint:

The half-life of a first-order reaction is constant and independent of initial concentration. Use \( t_{1/2} = \frac{0.693}{k} \).

Answer 1

The Correct Option is C

For a first-order reaction, the integrated rate law is: \[ k = \frac{2.303}{t} \log\left( \frac{[R]_0}{[R]} \right) \] For half-life, \( [R] = \frac{[R]_0}{2} \) Substitute into the equation: \[ t_{1/2} = \frac{2.303}{k} \log(2) = \frac{2.303 \times 0.3010}{k} = \frac{0.693}{k} \] Answer: \( \boxed{\frac{0.693}{k}} \)