Question

Calculate the rate constant of a reaction with a given half-life.

• A. \( k = \frac{0.693}{t_{1/2}} \)
• B. \( k = \frac{1}{t_{1/2}} \)
• C. \( k = \frac{2.303}{t_{1/2}} \)
• D. \( k = \frac{0.5}{t_{1/2}} \)

Hint:

For first-order reactions, remember that the half-life depends only on the rate constant and is given by \( t_{1/2} = \frac{0.693}{k} \).

Answer 1

The Correct Option is A

The relationship between the rate constant \( k \) and the half-life \( t_{1/2} \) is contingent upon the reaction order. For a first-order reaction, the half-life formula is as follows:
1. First-Order Reaction Half-Life: - The half-life of a first-order reaction is determined by the equation: \[ t_{1/2} = \frac{0.693}{k} \] - To express the rate constant \( k \) in terms of the half-life, the equation is rearranged to: \[ k = \frac{0.693}{t_{1/2}} \]2. Conclusion: - Consequently, the formula relating the rate constant \( k \) to the half-life \( t_{1/2} \) is \( k = \frac{0.693}{t_{1/2}} \).