Question

The half-life of a first-order reaction is 25 minutes. Its rate constant is:

• A. \( 2.27 \times 10^{-2} \, \text{min}^{-1} \)
• B. \( 3.2 \times 10^{-3} \, \text{min}^{-1} \)
• C. \( 9.2 \times 10^{-2} \, \text{min}^{-1} \)
• D. \( 2.8 \times 10^{-2} \, \text{min}^{-1} \)

Hint:

For a first-order reaction, the half-life is independent of the concentration of the reactant, and the rate constant can be calculated using the formula \( t_{1/2} = \frac{0.693}{k} \).

Answer 1

The Correct Option is A

For a first-order reaction, the relationship between the rate constant \( k \) and the half-life \( t_{1/2} \) is given by the equation: \[ t_{1/2} = \frac{0.693}{k} \] We are given that the half-life \( t_{1/2} \) is 25 minutes. Substituting the value into the equation, we can solve for \( k \): \[ 25 = \frac{0.693}{k} \] Solving for \( k \): \[ k = \frac{0.693}{25} = 2.77 \times 10^{-2} \, \text{min}^{-1} \]
Thus, the rate constant \( k \) is approximately \( 2.77 \times 10^{-2} \, \text{min}^{-1} \), which rounds to \( 2.27 \times 10^{-2} \, \text{min}^{-1} \).