Question

For a first-order reaction, the slope of the graph between \(\log[A]\) vs time is equal to:

• A. \(-\frac{k}{2.303}\)
• B. \(k\)
• C. \(2.303k\)
• D. \(-2.303k\)

Hint:

Remember: In a first-order reaction, the graph of \(\log[A]\) vs \(t\) is a straight line with slope \(-\frac{k}{2.303}\).

Answer 1

The Correct Option is A

For a first-order reaction, the integrated rate law is: \[ \log[A] = \log[A]_0 - \frac{k}{2.303} t \] This is in the form of a straight line equation: \[ y = c - mt \] where slope \( m = \frac{k}{2.303} \), and the negative sign indicates that the concentration decreases over time. Therefore, the slope of the graph of \(\log[A]\) vs time is: \[ -\frac{k}{2.303} \]