For a first order reaction, the rate constant k is given by
\(k = \frac{2.303}t \log\left(\frac{[A_0]}{[A]}\right)\)
where [A0] is the initial concentration of the reactant and [A] is the concentration of the reactant at time it
Rearranging this equation in the form . y = mx + c, we get
log [A0] – log [A] = \(\frac{kt}{2.303}\)
2.303 [log [A] – log [A]] = kt
log [A0] – log [A] = \(\frac{k}{2.303}t.\)
Hence a plot of log [A] vs t gives a straight line with a negative slope having the volume of \(\frac{-k}{2.303}\).
