For a reaction $\mathrm{A} \rightarrow \mathrm{P}$ at TK, the half life $(\mathrm{t}_{1/2})$ is plotted as a function of initial concentration $[\mathrm{A}]_{0}$ of A as given below: The value of x in the given figure is _____ s (Nearest integer)

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Chemical Kinetics

For a reaction

A \to P

at TK, the half life

(t_{1/2})

is plotted as a function of initial concentration

[A]_{0}

of A as given below:

The value of x in the given figure is _____ s
(Nearest integer)

Answer: 90

The plot of half-life against initial concentration is a straight line through the origin, so

t_{1/2} \propto [A]_{0}

. Since

t_{1/2} \propto [A]_{0}^{1 - n}

, this requires

1 - n = 1

, i.e. a zero-order reaction. Direct proportionality then lets the two points be compared:

\frac{x}{240} = \frac{1.5 \times 1 0 ^{- 3}}{4 \times 1 0 ^{- 3}}

, giving

x = \frac{240 \times 1.5}{4} = 90 s

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Integer answer