Question

In a reaction $A+B\rightarrow P$ rate is doubled when [B] is doubled, and the rate increases by 8 when both [A] and [B] are doubled. The rate law is:

• A. $r=k[A][B]$
• B. $r=k[A]^{2}[B]$
• C. $r=k[A][B]^{2}$
• D. $r=k[A][B]^{3}$

Hint:

Total factor = (Factor A)$^{order A} \times$ (Factor B)$^{order B}$. Here $8 = 2^x \times 2^1$.

Answer 1

The Correct Option is B

Step 1: Concept The rate law is $r = k[A]^{x}[B]^{y}$. We need to find orders $x$ and $y$.

Step 2: Meaning "Rate doubled when [B] is doubled" means $2 = 2^{y}$, so $y = 1$.

Step 3: Analysis "Rate increases by 8 when both are doubled" means $8 = 2^{x} \cdot 2^{y}$. Substituting $y = 1$: $8 = 2^{x} \cdot 2^{1} \Rightarrow 4 = 2^{x}$. This gives $x = 2$.

Step 4: Conclusion The rate law is $r = k[A]^{2}[B]^{1}$. This corresponds to option (B). Final Answer: (B)