Assume a general rate law

Let the rate law be $r = k[A]^m[B]^n$ where $m$ and $n$ are the orders with respect to $A$ and $B$.

Use experiments 1 and 2

From the table:

• Exp 1: $[A]=0.05,\, [B]=0.05,\, r=0.045$
• Exp 2: $[A]=0.10,\, [B]=0.05,\, r=0.090$

Here, $[B]$ is constant and $[A]$ is doubled.

Rate ratio: $\frac{0.090}{0.045}=2$

So, $2^m=2 \Rightarrow m=1$

Use experiments 2 and 3

From the table:

• Exp 2: $[A]=0.10,\, [B]=0.05,\, r=0.090$
• Exp 3: $[A]=0.20,\, [B]=0.10,\, r=0.72$

Both $[A]$ and $[B]$ are doubled.

Rate ratio: $\frac{0.72}{0.090}=8$

Therefore, $2^m \cdot 2^n = 8$ Since $m=1$, $2^1\cdot 2^n=8$ $2^{n+1}=2^3$ $n=2$

Write the rate law

Hence, $r = k[A]^1[B]^2$

So the rate law is $\boxed{\text{Rate} = k[A][B]^2}$

Check options

• A: $k[A][B]^2$ ✅
• B: $k[A]^2[B]^2$ ❌
• C: $k[A]^2[B]$ ❌
• D: $k[A][B]$ ❌

Comparison with stored answer

Stored correct answer: A

Derived answer: A

They match.