Domanda del libro di testo
Calculate the root mean square velocity and kinetic energy of CO, CO2, and SO3 at 298 K. Which gas has the greatest velocity? The greatest kinetic energy? The greatest effusion rate?
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Ch.5 - Gases
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving136
- Ch.2 - Atoms & Elements112
- Ch.3 - Molecules, Compounds & Chemical Equations159
- Ch.4 - Chemical Quantities & Aqueous Reactions140
- Ch.5 - Gases118
- Ch.6 - Thermochemistry106
- Ch.7 - Quantum-Mechanical Model of the Atom62
- Ch.8 - Periodic Properties of the Elements103
- Ch.9 - Chemical Bonding I: The Lewis Model104
- Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory89
- Ch.11 - Liquids, Solids & Intermolecular Forces73
- Ch.12 - Solids and Modern Material59
- Ch.13 - Solutions110
- Ch.14 - Chemical Kinetics140
- Ch.15 - Chemical Equilibrium78
- Ch.16 - Acids and Bases155
- Ch.17 - Aqueous Ionic Equilibrium176
- Ch.18 - Free Energy and Thermodynamics108
- Ch.19 - Electrochemistry118
- Ch.20 - Radioactivity and Nuclear Chemistry82
- Ch.21 - Organic Chemistry150
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Capitolo 5, Problema 83c
Calculate the root mean square velocity and kinetic energy of F2, Cl2, and Br2 at 298 K. Rank these three halogens with respect to their rate of effusion.
Guida verificata passo dopo passo1
Identify the formula for root mean square velocity: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(R\) is the ideal gas constant (8.314 J/mol·K), \(T\) is the temperature in Kelvin, and \(M\) is the molar mass in kg/mol.
Convert the molar masses of F\(_2\), Cl\(_2\), and Br\(_2\) from g/mol to kg/mol. F\(_2\) = 38.00 g/mol, Cl\(_2\) = 70.90 g/mol, Br\(_2\) = 159.80 g/mol.
Substitute the values of \(R\), \(T\), and \(M\) for each gas into the root mean square velocity formula to calculate \(v_{rms}\) for F\(_2\), Cl\(_2\), and Br\(_2\).
Use the kinetic energy formula \(KE = \frac{1}{2}mv^2\) to calculate the kinetic energy for each gas, where \(m\) is the molar mass in kg/mol and \(v\) is the root mean square velocity.
Apply Graham's law of effusion, which states that the rate of effusion is inversely proportional to the square root of the molar mass, to rank F\(_2\), Cl\(_2\), and Br\(_2\) in terms of their rate of effusion.
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Root Mean Square Velocity
The root mean square (RMS) velocity is a measure of the average 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 crucial for understanding how the speed of gas molecules relates to their mass and temperature.
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Percorso guidato
01:05
Root Mean Square Speed Formula
Kinetic Energy of Gases
The kinetic energy of gas molecules is directly related to their temperature and can be expressed using the formula KE = (1/2)mv^2, where m is the mass and v is the velocity of the gas particles. At a constant temperature, the average kinetic energy of gas molecules is the same, which allows for comparisons between different gases based on their molar masses.
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Percorso guidato
02:27Kinetic Energy Formulas
Graham's Law of Effusion
Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases effuse faster than heavier gases. Understanding this law is essential for ranking the rates of effusion of F2, Cl2, and Br2, as it allows us to predict which gas will effuse more quickly based on their respective molar masses.
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Percorso guidato
2:03Graham's Law of Effusion
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We separate U-235 from U-238 by fluorinating a sample of uranium to form UF6 (which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio of effusion rates for 238UF6 and 235UF6. The atomic mass of U-235 is 235.054 amu and that of U-238 is 238.051 amu.
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