A rate is equal to 0.0200 M/s. If [A] = 0.100M and rate = k[A]<, what is the new rate if the concentration of [A] is increased to 0.200 M?

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**Understanding Reaction Rates: Example Problem**

**Problem Statement:**
A rate is equal to 0.0200 M/s. If [A] = 0.100 M and the rate equation is given by rate = k[A]^2, what is the new rate if the concentration of [A] is increased to 0.200 M?

**Possible Answers:**
- ☐ 0.0200 M/s
- ☐ 0.100 M/s
- ☐ 0.0400 M/s
- ☐ 0.0600 M/s
- ☐ 0.0800 M/s

**Explanation:**
To solve this problem, you need to understand how the rate of a reaction changes with the concentration of a reactant. The given rate law is rate = k[A]^2, indicating that the rate of reaction is directly proportional to the square of the concentration of [A].

Given:
- Initial rate = 0.0200 M/s
- Initial concentration, [A] = 0.100 M
- Rate = k[A]^2

Firstly, determine the rate constant (k) using the provided data:
\[ 0.0200 \text{ M/s} = k \times (0.100 \text{ M})^2 \]
\[
0.0200 \text{ M/s} = k \times 0.0100 \text{ M}^2
\]
\[ 
k = \frac{0.0200 \text{ M/s}}{0.0100 \text{ M}^2} 
\]
\[ 
k = 2 \text{ M}^{-1}\text{s}^{-1} 
\]

Now, use this rate constant to find the new rate when [A] = 0.200 M:
\[ 
\text{New rate} = k \times (0.200 \text{ M})^2 
\]
\[ 
\text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times (0.200 \text{ M})^2 
\]
\[ 
\text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times 0.0400 \text{ M}^2 
\] 
\[ 
\text{New rate} = 0.080
Transcribed Image Text:**Understanding Reaction Rates: Example Problem** **Problem Statement:** A rate is equal to 0.0200 M/s. If [A] = 0.100 M and the rate equation is given by rate = k[A]^2, what is the new rate if the concentration of [A] is increased to 0.200 M? **Possible Answers:** - ☐ 0.0200 M/s - ☐ 0.100 M/s - ☐ 0.0400 M/s - ☐ 0.0600 M/s - ☐ 0.0800 M/s **Explanation:** To solve this problem, you need to understand how the rate of a reaction changes with the concentration of a reactant. The given rate law is rate = k[A]^2, indicating that the rate of reaction is directly proportional to the square of the concentration of [A]. Given: - Initial rate = 0.0200 M/s - Initial concentration, [A] = 0.100 M - Rate = k[A]^2 Firstly, determine the rate constant (k) using the provided data: \[ 0.0200 \text{ M/s} = k \times (0.100 \text{ M})^2 \] \[ 0.0200 \text{ M/s} = k \times 0.0100 \text{ M}^2 \] \[ k = \frac{0.0200 \text{ M/s}}{0.0100 \text{ M}^2} \] \[ k = 2 \text{ M}^{-1}\text{s}^{-1} \] Now, use this rate constant to find the new rate when [A] = 0.200 M: \[ \text{New rate} = k \times (0.200 \text{ M})^2 \] \[ \text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times (0.200 \text{ M})^2 \] \[ \text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times 0.0400 \text{ M}^2 \] \[ \text{New rate} = 0.080
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