A) A vessel at STP contains 28.5 kg of N2 (molecular mass = 28u). What is the mean free path of the N2 molecules in the vessel? An N2 molecule has a diameter of 3x10-10 m.
A) A vessel at STP contains 28.5 kg of N2 (molecular mass = 28u). What is the mean free path of the N2 molecules in the vessel? An N2 molecule has a diameter of 3x10-10 m.
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
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Problem Statement:**
A vessel at Standard Temperature and Pressure (STP) contains 28.5 kg of nitrogen gas (N₂) with a molecular mass of 28u (atomic mass units). What is the mean free path of the N₂ molecules in the vessel? An N₂ molecule has a diameter of 3 x 10⁻¹⁰ m.
**Solution Explanation:**
To find the mean free path of the nitrogen molecules, you need to understand the following concepts:
1. **Mean Free Path (λ):** The average distance traveled by a molecule between collisions.
2. **Formula for Mean Free Path:**
\[
\lambda = \frac{k_B \cdot T}{\sqrt{2} \cdot \pi \cdot d^2 \cdot P}
\]
Where:
- \( k_B \) is the Boltzmann constant (\(1.38 \times 10^{-23} \text{ J/K} \))
- \( T \) is the temperature in Kelvin
- \( d \) is the diameter of a molecule (given as \(3 \times 10^{-10} \) m)
- \( P \) is the pressure in Pascals (at STP, \( P = 1.013 \times 10^5 \) Pa)
- \( \pi \) is a constant (approximately 3.14159)
3. **Parameters at STP:**
- Temperature (\( T \) = 273.15 K)
- Pressure (\( P = 1.013 \times 10^5 \) Pa)
Plug the respective values into the formula to find the mean free path of N₂ molecules in the vessel.
By understanding these concepts, one can calculate physical properties like the mean free path which is crucial for understanding molecular dynamics in gases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03c32ca7-a243-40d2-963f-bc8ec9cda4bb%2F8d47da7e-ab26-43c1-9885-a1cd9177404b%2F6y7inv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A vessel at Standard Temperature and Pressure (STP) contains 28.5 kg of nitrogen gas (N₂) with a molecular mass of 28u (atomic mass units). What is the mean free path of the N₂ molecules in the vessel? An N₂ molecule has a diameter of 3 x 10⁻¹⁰ m.
**Solution Explanation:**
To find the mean free path of the nitrogen molecules, you need to understand the following concepts:
1. **Mean Free Path (λ):** The average distance traveled by a molecule between collisions.
2. **Formula for Mean Free Path:**
\[
\lambda = \frac{k_B \cdot T}{\sqrt{2} \cdot \pi \cdot d^2 \cdot P}
\]
Where:
- \( k_B \) is the Boltzmann constant (\(1.38 \times 10^{-23} \text{ J/K} \))
- \( T \) is the temperature in Kelvin
- \( d \) is the diameter of a molecule (given as \(3 \times 10^{-10} \) m)
- \( P \) is the pressure in Pascals (at STP, \( P = 1.013 \times 10^5 \) Pa)
- \( \pi \) is a constant (approximately 3.14159)
3. **Parameters at STP:**
- Temperature (\( T \) = 273.15 K)
- Pressure (\( P = 1.013 \times 10^5 \) Pa)
Plug the respective values into the formula to find the mean free path of N₂ molecules in the vessel.
By understanding these concepts, one can calculate physical properties like the mean free path which is crucial for understanding molecular dynamics in gases.
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