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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![**Exercise: Root-Mean-Square Speed of Argon Molecules**
Calculate the root-mean-square speed of \( \text{Ar} \) (Argon) molecules in a sample of argon gas at a temperature of 106°C.
\[ \text{Root-Mean-Square Speed} = \quad \boxed{} \quad \text{m s}^{-1} \]
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Transcribed Image Text:**Exercise: Root-Mean-Square Speed of Argon Molecules**
Calculate the root-mean-square speed of \( \text{Ar} \) (Argon) molecules in a sample of argon gas at a temperature of 106°C.
\[ \text{Root-Mean-Square Speed} = \quad \boxed{} \quad \text{m s}^{-1} \]
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[Submit Answer]
![### Ideal Gas Law and van der Waals Equation Comparison
**Problem Statement:**
According to the ideal gas law, a 1.072 mol sample of nitrogen gas in a 1.882 L container at 269.5 K should exert a pressure of 12.60 atm. What is the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure? For \( N_2 \) gas, the constants are:
\[ a = 1.390 \frac{L^2 \cdot atm}{mol^2} \]
\[ b = 0.03910 \frac{L}{mol} \]
**Formula for Percent Difference:**
The percent difference is calculated using the following formula:
\[
\text{Percent difference} = \left| \frac{P_{\text{ideal}} - P_{\text{van der Waals}}}{\left( \frac{P_{\text{ideal}} + P_{\text{van der Waals}}}{2} \right)} \right| \times 100
\]
**Calculation Input Fields:**
\[
\text{Percent difference} = \_\_\_\_\_\_ \%
\]
### Explanation of Graphs and Diagrams
*There are no graphs or diagrams in the text provided.*
### Detailed Steps
1. **Determine the Ideal Gas Pressure (\( P_{\text{ideal}} \))**:
- Given by the problem statement as 12.60 atm.
2. **Calculate the Pressure Using van der Waals' Equation (\( P_{\text{van der Waals}} \))**:
- Use the van der Waals' equation to find \( P_{\text{van der Waals}} \).
\[
\left( P + \frac{a n^2}{V^2} \right) (V - nb) = nRT
\]
where:
- \( n \) = 1.072 mol
- \( V \) = 1.882 L
- \( T \) = 269.5 K
- \( R \) = 0.0821 L atm / (K mol)
- \( a \) and \( b \) are constants provided for \( N_2 \) gas.
3. **Apply the Percent Difference Formula**:
- Plug values of \( P_{\text](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3dc4344c-ea94-4ce1-bf5f-fb050c5965fa%2Faa7bfa62-309f-47d7-b3ed-d03bbbfafc06%2Fbcrmx8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Ideal Gas Law and van der Waals Equation Comparison
**Problem Statement:**
According to the ideal gas law, a 1.072 mol sample of nitrogen gas in a 1.882 L container at 269.5 K should exert a pressure of 12.60 atm. What is the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure? For \( N_2 \) gas, the constants are:
\[ a = 1.390 \frac{L^2 \cdot atm}{mol^2} \]
\[ b = 0.03910 \frac{L}{mol} \]
**Formula for Percent Difference:**
The percent difference is calculated using the following formula:
\[
\text{Percent difference} = \left| \frac{P_{\text{ideal}} - P_{\text{van der Waals}}}{\left( \frac{P_{\text{ideal}} + P_{\text{van der Waals}}}{2} \right)} \right| \times 100
\]
**Calculation Input Fields:**
\[
\text{Percent difference} = \_\_\_\_\_\_ \%
\]
### Explanation of Graphs and Diagrams
*There are no graphs or diagrams in the text provided.*
### Detailed Steps
1. **Determine the Ideal Gas Pressure (\( P_{\text{ideal}} \))**:
- Given by the problem statement as 12.60 atm.
2. **Calculate the Pressure Using van der Waals' Equation (\( P_{\text{van der Waals}} \))**:
- Use the van der Waals' equation to find \( P_{\text{van der Waals}} \).
\[
\left( P + \frac{a n^2}{V^2} \right) (V - nb) = nRT
\]
where:
- \( n \) = 1.072 mol
- \( V \) = 1.882 L
- \( T \) = 269.5 K
- \( R \) = 0.0821 L atm / (K mol)
- \( a \) and \( b \) are constants provided for \( N_2 \) gas.
3. **Apply the Percent Difference Formula**:
- Plug values of \( P_{\text
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