Question

If for a reaction, \(A+B\rightarrow C+D\), when \([A]\) alone is doubled, the rate gets doubled and when \([B]\) alone is increased by \(9\) times, the rate gets tripled. Find the order of reaction.

• A. \(3/4\)
• B. \(3/2\)
• C. \(4/9\)
• D. \(2\)

Hint:

Write the rate law with unknown partial orders and use the two given rate changes to find each order.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Assume the rate law \(r=k[A]^{x}[B]^{y}\). The overall order of the reaction is \(x+y\).

Step 2: Effect of doubling [A]
When \([A]\) is doubled, the rate also doubles.
\(2^{x}=2\), so \(x=1\).

Step 3: Effect of increasing [B]
When \([B]\) becomes 9 times, the rate becomes 3 times.
\(9^{y}=3\), so \(y=\dfrac{1}{2}\).

Step 4: Overall order
Order \(=x+y=1+\dfrac{1}{2}=\dfrac{3}{2}\).

Final Answer:
The overall order of the reaction is 3/2. \[ \boxed{\text{(B) }\dfrac{3}{2}} \]