Question

Choose the correct statement.

• A. The plot of \( [A] \) versus time \( t \) for a zero order reaction is a horizontal line parallel to the x-axis which represents \( t \).
• B. For a first order reaction the time taken for \( \frac{3}{4}^{\text{th}} \) completion is 2 times the half-life period.
• C. For a second order reaction the rate of reaction with respect to reactant becomes 27 times when its concentration is tripled.
• D. Molecularity of a chemical reaction is always greater than order of the reaction.

Hint:

For first order reactions, time for 75% completion is always \( 2t_{1/2} \). Also remember graph shapes for zero, first and second order reactions.

Answer 1

The Correct Option is B

Step 1: Analyze option (A).
For a zero order reaction:
\[ [A] = [A]_0 - kt \]
The graph of \( [A] \) vs \( t \) is a straight line with negative slope, not horizontal.
So, (A) is incorrect.

Step 2: Analyze option (B).
For a first order reaction:
Half-life:
\[ t_{1/2} = \frac{0.693}{k} \]
For \( \frac{3}{4} \) completion, remaining concentration = \( \frac{1}{4}[A]_0 \):
\[ t = \frac{2.303}{k}\log 4 = \frac{2.303}{k} \times 0.602 \]
\[ t \approx \frac{1.386}{k} = 2 \times \frac{0.693}{k} \]
\[ t = 2t_{1/2} \]
So, (B) is correct.

Step 3: Analyze option (C).
For second order reaction:
\[ \text{Rate} \propto [A]^2 \]
If concentration is tripled:
\[ \text{Rate} = 3^2 = 9 \text{ times} \]
Not 27 times. So, (C) is incorrect.

Step 4: Analyze option (D).
Molecularity is defined for elementary reactions and is always a whole number.
Order can be zero, fractional or even negative.
So, molecularity is not always greater than order.
Thus, (D) is incorrect.

Step 5: Final conclusion.
\[ \boxed{\text{Option (B) is correct}} \]