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Compute the root-mean-square speed of Ar molecules in a sample of argon gas at a temperature of 106°C. Submit Answer m s 1

Compute the root-mean-square speed of Ar molecules in a sample of argon gas at a temperature of 106°C. Submit Answer m s 1

Chemistry
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. \[ \text{Root-Mean-Square Speed} = \quad \boxed{} \quad \text{m s}^{-1} \] Click the button to submit your answer: [Submit Answer]
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. \[ \text{Root-Mean-Square Speed} = \quad \boxed{} \quad \text{m s}^{-1} \] Click the button to submit your answer: [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
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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