Question

Relation between $t_{1/2}$ & $t_{100\%}$ for zero order & Ist order reaction respectively is:

• A. $t_{100\%} = 2 \times t_{1/2} : t_{100\%} = 2 \times t_{1/2}$
• B. $t_{100\%} = 2 \times t_{1/2} : t_{100\%} = t_{1/2}$
• C. $t_{100\%} = 2 \times t_{1/2} : t_{100\%} = \infty$
• D. $t_{100\%} = \infty : t_{100\%} = 2 \times t_{1/2}$

Answer 1

The Correct Option is C

Comparison of completion times for different reaction orders.

ZERO ORDER ANALYSIS:
The rate of a zero-order reaction is constant. If it takes a certain amount of time to consume half the reactant, it will take exactly the same amount of time to consume the remaining half. Thus, total time ($t_{100\%}$) is twice the half-life ($t_{1/2}$).
$t_{100\%} = 2 \cdot t_{1/2}$

FIRST ORDER ANALYSIS:
The rate of a first-order reaction decreases as the reactant is consumed. Theoretically, the amount of reactant decreases exponentially but never truly reaches zero in finite time.
Formula: $t = \frac{1}{k} \ln\left(\frac{[A]_0}{[A]_t}\right)$
For $[A]_t = 0$, $t = \frac{1}{k} \ln(\infty) = \infty$.
Thus, $t_{100\%} = \infty$.

RESULT:
Matching the logic with the options leads to (3).