To determine the rate of the reaction that follows the rate law [tex]\( \text{rate} = k[A]^m[B]^n \)[/tex], we need to substitute the given values into the rate equation and compute the result step-by-step.
Given values:
- The rate constant [tex]\( k = 1.5 \)[/tex]
- The concentration of reactant A, [tex]\( [A] = 1 \, \text{M} \)[/tex]
- The concentration of reactant B, [tex]\( [B] = 3 \, \text{M} \)[/tex]
- The order of the reaction with respect to A, [tex]\( m = 2 \)[/tex]
- The order of the reaction with respect to B, [tex]\( n = 1 \)[/tex]
The rate law can be expressed as:
[tex]\[ \text{rate} = k[A]^m[B]^n \][/tex]
Now, substituting the given values:
[tex]\[ \text{rate} = 1.5 \times (1)^{2} \times (3)^{1} \][/tex]
Let's break this down further:
1. Calculate [tex]\([A]^m\)[/tex]:
[tex]\[ [A]^m = (1)^2 = 1 \][/tex]
2. Calculate [tex]\([B]^n\)[/tex]:
[tex]\[ [B]^n = (3)^1 = 3 \][/tex]
3. Now, multiply these results with the rate constant [tex]\( k \)[/tex]:
[tex]\[ \text{rate} = 1.5 \times 1 \times 3 \][/tex]
4. Perform the multiplication:
[tex]\[ \text{rate} = 1.5 \times 3 = 4.5 \][/tex]
Therefore, the rate of the reaction is [tex]\( 4.5 \, (\text{mol/L})/\text{s} \)[/tex].
The correct answer is:
C. [tex]\( 4.5 \, (\text{mol/L})/\text{s} \)[/tex]
