To find the rate of the reaction, we can use the provided rate equation:
[tex]\[ \text{Rate} = k[A]^2[B]^2 \][/tex]
Given the values:
- [tex]\( k = 0.1 \, \text{(rate constant)} \)[/tex]
- [tex]\( [A] = 1 \, \text{M} \)[/tex]
- [tex]\( [B] = 2 \, \text{M} \)[/tex]
Let's substitute these values into the rate equation step-by-step:
1. Substitute the concentration values and the rate constant into the rate equation:
[tex]\[
\text{Rate} = 0.1 \times (1)^2 \times (2)^2
\][/tex]
2. Calculate [tex]\( [A]^2 \)[/tex]:
[tex]\[
[A]^2 = (1)^2 = 1
\][/tex]
3. Calculate [tex]\( [B]^2 \)[/tex]:
[tex]\[
[B]^2 = (2)^2 = 4
\][/tex]
4. Multiply all the terms together:
[tex]\[
\text{Rate} = 0.1 \times 1 \times 4 = 0.4
\][/tex]
So, the rate of the reaction is:
[tex]\[
\text{Rate} = 0.4 \, \text{(mol/L)/s}
\][/tex]
Therefore, the correct answer is:
D. [tex]\( 0.4 \, \text{(mol/L)/s} \)[/tex]
