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

The integrated rate law for a first-order reaction is expressed as: \[ \log[A] = \log[A]_0 - \frac{k}{2.303} t \] This equation aligns with the linear form \( y = c - mt \). In this context, the slope \( m \) is \( \frac{k}{2.303} \). The negative sign signifies a reduction in concentration over time. Consequently, the slope of the plot of \(\log[A]\) against time is: \[ -\frac{k}{2.303} \]