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What is the rate of a reaction if the value of [tex]\( k \)[/tex] is [tex]\( 0.1 \, \text{M}^{-3} \text{s}^{-1} \)[/tex], [tex]\([A]\)[/tex] is [tex]\( 1 \, \text{M} \)[/tex], and [tex]\([B]\)[/tex] is [tex]\( 2 \, \text{M} \)[/tex]?

[tex]\[
\text{Rate} = k[A]^2[B]^2
\][/tex]

A. [tex]\( 0.8 \, \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \)[/tex]

B. [tex]\( 1.6 \, \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \)[/tex]

C. [tex]\( 0.2 \, \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \)[/tex]

D. [tex]\( 0.4 \, \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \)[/tex]



Answer :

GinnyAnswer
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]

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