To determine the rate of the reaction given the rate law:
[tex]\[ \text{rate} = k[A]^m[B]^n \][/tex]
We are provided with the following parameters:
- [tex]\( k = 1 \times 10^{-2} \)[/tex]
- [tex]\([A] = 2 \, \text{M} \)[/tex]
- [tex]\([B] = 3 \, \text{M} \)[/tex]
- [tex]\( m = 2 \)[/tex]
- [tex]\( n = 1 \)[/tex]
Let's follow the steps to calculate the reaction rate:
1. Substitute the given concentrations and orders into the rate law equation:
[tex]\[ \text{rate} = k[A]^m[B]^n \][/tex]
2. Insert the values for [tex]\( k \)[/tex], [tex]\([A] \)[/tex], [tex]\([B] \)[/tex], [tex]\( m \)[/tex], and [tex]\( n \)[/tex]:
[tex]\[ \text{rate} = (1 \times 10^{-2}) \times (2)^2 \times (3)^1 \][/tex]
3. Calculate [tex]\([A]^m\)[/tex]:
[tex]\[ [A]^m = (2)^2 = 4 \][/tex]
4. Calculate [tex]\([B]^n\)[/tex]:
[tex]\[ [B]^n = (3)^1 = 3 \][/tex]
5. Multiply these values together along with the rate constant [tex]\( k \)[/tex]:
[tex]\[ \text{rate} = (1 \times 10^{-2}) \times 4 \times 3 \][/tex]
6. Do the multiplication:
[tex]\[ \text{rate} = (1 \times 10^{-2}) \times 12 \][/tex]
7. Finally, compute the result:
[tex]\[ \text{rate} = 0.12 \, \text{mol/(L \cdot s)} \][/tex]
Therefore, the rate of the reaction is [tex]\(\boxed{0.12 \, \text{mol/(L \cdot s)}}\)[/tex]. The correct answer is:
B. [tex]\( 0.12 \, \text{mol/(L \cdot s)} \)[/tex]
