Read the passage carefully and answer the questions.

The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time $t$ is related with its initial concentration by the relation, $C = C_0e^{-kt}$. The rate constants for different orders have different expressions. For a first order reaction, $k =\frac{2.303}{t}\log\frac{a}{a-x}$, where $a$ is the initial concentration and $x$ is the extent of reaction.

Which plot is linear with negative slope for a first order reaction

ln[C] versus time

The correct answer is Option (4) → ln[C] versus time

For a first-order reaction, the integrated rate law is:

$[C] = [C]_0 e^{-kt} ⇒\ln[C] = \ln[C]_0 – kt$

• This is in the form $y = mx + c$, where:
• $y = \ln[C]$
• $x=t$
• slope $m=−k$ (negative)

✅ So, a plot of $\ln[C]$ versus time is linear with a negative slope.