Question

What will be the order of the reaction when the initial concentration is doubled the time of half reaction is doubled?

• A. Third
• B. Second
• C. Zero
• D. First

Hint:

For zero order reaction: \[ t_{1/2}\propto [A]_0 \] So if initial concentration doubles, half-life also doubles.

Answer 1

The Correct Option is C

Concept:
The half-life of a reaction is the time required for the concentration of reactant to become half of its initial value. The dependence of half-life on initial concentration helps identify the order of reaction. For a zero order reaction: \[ t_{1/2}=\frac{[A]_0}{2k} \] For a first order reaction: \[ t_{1/2}=\frac{0.693}{k} \]

Step 1: Observe the given condition.
The question says: When initial concentration is doubled, the half-life is also doubled. So: \[ [A]_0 \rightarrow 2[A]_0 \] and: \[ t_{1/2} \rightarrow 2t_{1/2} \] This means: \[ t_{1/2}\propto [A]_0 \]

Step 2: Compare with zero order reaction.
For zero order reaction: \[ t_{1/2}=\frac{[A]_0}{2k} \] Here: \[ t_{1/2}\propto [A]_0 \] So if initial concentration is doubled, half-life also doubles.

Step 3: Compare with first order reaction.
For first order reaction: \[ t_{1/2}=\frac{0.693}{k} \] It is independent of initial concentration. So first order is not correct.

Step 4: Check the options.
Option (A) Third is incorrect.
Option (B) Second is incorrect.
Option (C) Zero is correct.
Option (D) First is incorrect because first order half-life does not depend on initial concentration. Hence, the correct answer is: \[ \boxed{(C)\ \text{Zero}} \]