Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Determining the Units of the Rate Constant \( k \) in Various Rate Laws
2. **What are the units of the rate constant, \( k \), in the following rate laws?**
For the given rate laws, determine the units of the rate constant, \( k \):
1. **First Rate Law:**
\[\text{rate} = k [A]^2 [B]\]
2. **Second Rate Law:**
\[\text{rate} = k [A][B]\]
3. **Third Rate Law:**
\[\text{rate} = k [A]^0\]
**Explanation:**
- The rate of a chemical reaction is generally given in units of concentration per unit time (e.g., \( \text{M/s} \) where \( \text{M} \) stands for molarity, or moles per liter).
- \( [A] \) and \( [B] \) represent concentrations of reactants, commonly expressed in molarity (M).
To find the units of \( k \) for each rate law, we will equate the units on both sides of the rate law equations.
1. **For the first rate law:**
\[\text{Units of rate} = \text{Units of } k \cdot (\text{Units of } [A])^2 \cdot (\text{Units of } [B])\]
\[\text{M/s} = k \cdot (\text{M})^2 \cdot (\text{M})\]
\[\text{M/s} = k \cdot \text{M}^3\]
\[k = \frac{\text{M/s}}{\text{M}^3}\]
\[k = \text{M}^{-2}\text{s}^{-1}\]
2. **For the second rate law:**
\[\text{Units of rate} = \text{Units of } k \cdot (\text{Units of } [A]) \cdot (\text{Units of } [B])\]
\[\text{M/s} = k \cdot \text{M} \cdot \text{M}\]
\[\text{M/s} = k \cdot \text{M}^2\]
\[k = \frac{\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7442e5-ed1a-4154-ba5d-4813abad6cff%2Ff0582ceb-9ea0-4f23-bebe-5b3eaad9beb1%2Fhvbqk4n.png&w=3840&q=75)
Transcribed Image Text:### Determining the Units of the Rate Constant \( k \) in Various Rate Laws
2. **What are the units of the rate constant, \( k \), in the following rate laws?**
For the given rate laws, determine the units of the rate constant, \( k \):
1. **First Rate Law:**
\[\text{rate} = k [A]^2 [B]\]
2. **Second Rate Law:**
\[\text{rate} = k [A][B]\]
3. **Third Rate Law:**
\[\text{rate} = k [A]^0\]
**Explanation:**
- The rate of a chemical reaction is generally given in units of concentration per unit time (e.g., \( \text{M/s} \) where \( \text{M} \) stands for molarity, or moles per liter).
- \( [A] \) and \( [B] \) represent concentrations of reactants, commonly expressed in molarity (M).
To find the units of \( k \) for each rate law, we will equate the units on both sides of the rate law equations.
1. **For the first rate law:**
\[\text{Units of rate} = \text{Units of } k \cdot (\text{Units of } [A])^2 \cdot (\text{Units of } [B])\]
\[\text{M/s} = k \cdot (\text{M})^2 \cdot (\text{M})\]
\[\text{M/s} = k \cdot \text{M}^3\]
\[k = \frac{\text{M/s}}{\text{M}^3}\]
\[k = \text{M}^{-2}\text{s}^{-1}\]
2. **For the second rate law:**
\[\text{Units of rate} = \text{Units of } k \cdot (\text{Units of } [A]) \cdot (\text{Units of } [B])\]
\[\text{M/s} = k \cdot \text{M} \cdot \text{M}\]
\[\text{M/s} = k \cdot \text{M}^2\]
\[k = \frac{\
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