For a first-order reaction $\mathbf{R} \rightarrow \mathbf{P}$ at a given temperature, $k$ is the rate constant. For this reaction, at the given temperature, the concentrations of $\mathbf{R}$ and $\mathbf{P}$ at a time $t$ are $[\mathbf{R}]$ and $[\mathbf{P}]$, respectively. The correct graphical representation(s) for this reaction is(are)

(C) (see structure); (D) (see structure)

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Chemical Kinetics

For a first-order reaction

R \to P

at a given temperature,

k

is the rate constant. For this reaction, at the given temperature, the concentrations of

R

and

P

at a time

t

are

[R]

and

[P]

, respectively. The correct graphical representation(s) for this reaction is(are)

Answer: (C), (D)

For a first-order reaction

R \to P

:

Option (A):

[P]_{t} = [R]_{0} (1 - e^{- k t})

shows an exponential rise, not a straight line. Incorrect.

Option (B):

\frac{d [ R ]}{d t} = - k [R]

means the rate vs [R] plot should pass through origin with negative slope. The graph shown doesn't match. Incorrect.

Option (C): Rate

= \frac{d [ P ]}{d t} = k [R]_{0} e^{- k t}

. This shows an exponential decay of rate with time, which is correct for a first-order reaction.

Option (D): For a first-order reaction,

k

is constant and independent of concentration or time. A horizontal line at constant

k

is correct.

Therefore, options (C) and (D) are correct.

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · One or more correct options