To determine the rate of the reaction given the rate law [tex]\( \text{rate} = k[A]^m[B]^n \)[/tex], we need to follow these steps:
1. Identify the constants and reactant concentrations:
- Rate constant [tex]\( k = 0.2 \)[/tex]
- Concentration of [tex]\( A \)[/tex], denoted as [tex]\([A] = 3 \, \text{M}\)[/tex]
- Concentration of [tex]\( B \)[/tex], denoted as [tex]\([B] = 3 \, \text{M}\)[/tex]
- Order of reaction with respect to [tex]\( A \)[/tex], denoted as [tex]\( m = 1 \)[/tex]
- Order of reaction with respect to [tex]\( B \)[/tex], denoted as [tex]\( n = 2 \)[/tex]
2. Substitute the identified values into the rate law formula:
[tex]\[
\text{rate} = k[A]^m[B]^n
\][/tex]
Using the given values:
[tex]\[
\text{rate} = 0.2 \times (3)^1 \times (3)^2
\][/tex]
3. Calculate the individual powers and multiplications:
- Calculate [tex]\( (3)^1 \)[/tex]:
[tex]\[
(3)^1 = 3
\][/tex]
- Calculate [tex]\( (3)^2 \)[/tex]:
[tex]\[
(3)^2 = 9
\][/tex]
- Multiply these results with the rate constant [tex]\( k \)[/tex]:
[tex]\[
\text{rate} = 0.2 \times 3 \times 9
\][/tex]
4. Multiply the numbers step by step:
- First, multiply [tex]\( 3 \times 9 \)[/tex]:
[tex]\[
3 \times 9 = 27
\][/tex]
- Then, multiply this result by [tex]\( 0.2 \)[/tex]:
[tex]\[
0.2 \times 27 = 5.4
\][/tex]
Therefore, the rate of the reaction is [tex]\( 5.4 \, \text{(mol/L)/s} \)[/tex].
The correct answer is:
B. [tex]\( 5.4 \, \text{(mol/L)/s} \)[/tex]
