For first-order reactions, remember that the slope of the log(concentration) vs. time plot is always \(\frac{-k}{2.303}\).
For a first-order reaction, the integrated rate law is:
\( \ln[A] = -kt + \ln[A]_0 \)
where [A] is the concentration at time t, k is the rate constant, and \([A]_0\) is the initial concentration. Using base-10 logarithms:
\( \log[A] = \frac{-k}{2.303}t + \log[A]_0 \)
This equation resembles \(y = mx + c\), where:
- \(y = \log[A]\),
- \(x = t\),
- \(m = \frac{-k}{2.303}\),
- \(c = \log[A]_0\).
Therefore, the slope of a plot of log(reactant concentration) versus time is \(\frac{-k}{2.303}\).