JEE Main 2026 — Apr 2, Shift 1 — Chemistry solution

JEE Main2026Apr 2, Shift 1Chemistry

$t_{100%}$ is the time required for the $100%$ completion of the reaction while $t_{1/2}$ is the time required for $50%$ of the reaction to be completed. Which of the following option correctly represents the relation between $t_{100%}$ and $t_{1/2}$ for zero and first order reactions respectively ?

A
$t_{100%} = (t_{1/2})^{2}$ and $t_{100%} = (t_{1/2})^{- \infty}$
B
$t_{100%} = 2 t_{1/2}$ and $t_{100%} = (t_{1/2})^{\infty}$
C
$t_{100%} = 2 t_{1/2}$ and $t_{100%} = (2 t_{1/2})^{2}$
D
$t_{100%} = (t_{1/2})^{\infty}$ and $t_{100%} = 2 t_{1/2}$

Solution

Zero order: $[A] = [A]_{0} - k t$ . Setting $[A] = 0$ gives $t_{100%} = [A]_{0} / k$ , and $t_{1/2} = [A]_{0} / (2 k)$ . Therefore $t_{100%} = 2 t_{1/2}$ .

First order: $[A] = [A]_{0} e^{- k t}$ never reaches zero in finite time, so $t_{100%} \to \infty$ . Since $t_{1/2} = ln 2/ k$ is finite, the formal relation is $t_{100%} = (t_{1/2})^{\infty}$ .

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