What is the rate constant k for a first-order reaction if its half-life is 2.50 min?

• A. 0.693 min^{-1}
• B. 0.173 min^{-1}
• C. 0.277 min^{-1}
• D. 0.400 min^{-1}

Answer: (C)

Verified step by step guidance

1. Recall the relationship between the half-life (\(t_{1/2}\)) and the rate constant (\(k\)) for a first-order reaction, which is given by the formula: \[t_{1/2} = \frac{0.693}{k}\]
2. Rearrange the formula to solve for the rate constant \(k\): \[k = \frac{0.693}{t_{1/2}}\]
3. Substitute the given half-life value (\(t_{1/2} = 2.50\) min) into the equation: \[k = \frac{0.693}{2.50 \text{ min}}\]
4. Perform the division to find the numerical value of \(k\) (do not calculate the final number here, just set up the expression).
5. Express the units of \(k\) correctly for a first-order reaction, which are inverse time units (e.g., min\(^{-1}\)).