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Determine the rate of a reaction that follows the rate law: rate [tex]=k[A]^m[B]^n[/tex], where:

[tex]\[
\begin{array}{l}
k = 1.5 \\
[A] = 1 \, M \\
[B] = 3 \, M \\
m = 2 \\
n = 1
\end{array}
\][/tex]

A. [tex]13.5 \, (mol/L \cdot s)[/tex]
B. [tex]9.0 \, (mol/L \cdot s)[/tex]
C. [tex]4.5 \, (mol/L \cdot s)[/tex]
D. [tex]1.5 \, (mol/L \cdot s)[/tex]


Sagot :

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]