Question

The rate of a reaction doubles when the initial concentration of the reactant is made fourfold. If the initial concentration is made 400 fold, then the rate will become:

• A. 400 times
• B. 200 times
• C. 40 times
• D. 20 times

Hint:

If rate doubles for 4× concentration \(\Rightarrow\) order = \(1/2\).

Answer 1

The Correct Option is D

Concept: \[ \text{Rate} \propto [A]^n \]

Step 1: Find order \(n\).
\[ 2 = 4^n \Rightarrow 2 = (2^2)^n = 2^{2n} \Rightarrow 2n = 1 \Rightarrow n = \frac{1}{2} \]

Step 2: New concentration.
\[ \text{Rate} \propto (400)^{1/2} = 20 \]