Domanda del libro di testo
What are the basic assumptions of the kinetic–molecular
theory?
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Ch.10 - Gases: Their Properties & Behavior
McMurry8th EditionChemistryISBN: 9781292336145
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TOC.tableOfContents
- Ch.1 - Chemical Tools: Experimentation & Measurement170
- Ch.2 - Atoms, Molecules & Ions160
- Ch.3 - Mass Relationships in Chemical Reactions169
- Ch.4 - Reactions in Aqueous Solution199
- Ch.5 - Periodicity & Electronic Structure of Atoms102
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory92
- Ch.7 - Covalent Bonding and Electron-Dot Structures61
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure59
- Ch.9 - Thermochemistry: Chemical Energy122
- Ch.10 - Gases: Their Properties & Behavior155
- Ch.11 - Liquids & Phase Changes54
- Ch.12 - Solids and Solid-State Materials73
- Ch.13 - Solutions & Their Properties120
- Ch.14 - Chemical Kinetics98
- Ch.15 - Chemical Equilibrium125
- Ch.16 - Aqueous Equilibria: Acids & Bases110
- Ch.17 - Applications of Aqueous Equilibria147
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium86
- Ch.19 - Electrochemistry154
- Ch.20 - Nuclear Chemistry96
- Ch.21 - Transition Elements and Coordination Chemistry156
- Ch.22 - The Main Group Elements187
- Ch.23 - Organic and Biological Chemistry51
Capitolo 10, Problema 94
The average temperature at an altitude of 20 km is 220 K. What is the average speed in m/s of an N2 molecule at this altitude?
Guida verificata passo dopo passo1
Identify the formula for the average speed of a gas molecule, which is given by the equation: \( v_{avg} = \sqrt{\frac{8kT}{\pi m}} \), where \( k \) is the Boltzmann constant, \( T \) is the temperature in Kelvin, and \( m \) is the mass of a single molecule.
Convert the mass of an \( \text{N}_2 \) molecule from grams per mole to kilograms per molecule. Start by finding the molar mass of \( \text{N}_2 \), which is approximately 28.02 g/mol, and then convert it to kg by dividing by 1000.
Use Avogadro's number \( 6.022 \times 10^{23} \) to convert the molar mass in kg/mol to kg/molecule by dividing the mass in kg/mol by Avogadro's number.
Substitute the values into the formula: \( k = 1.38 \times 10^{-23} \text{ J/K} \), \( T = 220 \text{ K} \), and the calculated mass of an \( \text{N}_2 \) molecule in kg.
Calculate the average speed \( v_{avg} \) using the substituted values to find the result in meters per second.
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Kinetic Molecular Theory
Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It states that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas in Kelvin. This theory helps us understand how temperature affects the speed of gas molecules, which is crucial for calculating the average speed of an N2 molecule at a given temperature.
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Percorso guidato
01:19
Kinetic Molecular Theory
Root Mean Square Speed
The root mean square (RMS) speed is a statistical measure of the speed of particles in a gas. It is calculated using the formula v_rms = sqrt(3RT/M), where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. This concept is essential for determining the average speed of nitrogen molecules at the specified altitude and temperature.
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01:05Root Mean Square Speed Formula
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. While the question focuses on molecular speed, understanding the Ideal Gas Law provides context for how gases behave under different conditions, including temperature and altitude, which can influence molecular motion and speed.
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01:15Ideal Gas Law Formula
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