Question

In a first order reaction, when $log\left[\frac{a}{(a-x)}\right]$ ($a$ is the initial reactant concentration and $x$ is the amount reacted) is plotted against time, the graph obtained is:

• A. a straight line with a negative slope
• B. a straight line having slope $\frac{k}{2.303}$
• C. a straight line having slope $\frac{-k}{2.303}$
• D. an asymptotic curve

Answer 1

Answer: (B)

a straight line having slope $\frac{k}{2.303}$

The integrated rate law for the first order reaction is $k=\frac{2.303}{t}\log \frac{a}{a-x}$.

This equation can be rearranged as $\log \frac{a-x}{a}=\frac{kt}{2.303}+0$. It is the form of straight line $y=mx+c$.

Hence, in a first order reaction, when $log\left[\frac{a}{(a-x)}\right]$ is plotted against time, the graph obtained is a straight line having the slope $\frac{k}{2.303}.$