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Ch 18: Thermal Properties of Matter
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 18: Thermal Properties of MatterProblem 31a
Chapter 18, Problem 31a

Oxygen (O2) has a molar mass of 32.0 32.0 g/mol. What is the average translational kinetic energy of an oxygen molecule at a temperature of 300300 K?

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Start by understanding the concept of translational kinetic energy for a molecule. The average translational kinetic energy of a molecule in a gas is given by the formula: 3kT2, where k is the Boltzmann constant and T is the temperature in Kelvin.
Identify the values needed for the calculation. The temperature T is given as 300 K. The Boltzmann constant k is approximately 1.38×10-23J·K-1.
Substitute the values into the formula for average translational kinetic energy: 3×1.38×10-23×3002.
Perform the multiplication in the numerator: 3×1.38×10-23×300.
Divide the result from the previous step by 2 to find the average translational kinetic energy of an oxygen molecule at 300 K.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Theory of Gases

The kinetic theory of gases explains the behavior of gases in terms of the motion of their molecules. It states that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas. This concept is crucial for understanding how temperature affects the energy of molecules in a gas.
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Translational Kinetic Energy

Translational kinetic energy refers to the energy due to the motion of a molecule moving from one place to another. For a single molecule, it is given by the formula (3/2)kT, where k is the Boltzmann constant and T is the temperature in Kelvin. This concept helps in calculating the energy associated with the movement of molecules at a given temperature.
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Boltzmann Constant

The Boltzmann constant (k) is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. Its value is approximately 1.38 x 10^-23 J/K. Understanding this constant is essential for calculating the average kinetic energy of molecules in a gas at a specific temperature.
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Related Practice
Textbook Question

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element.)

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Textbook Question

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare the average kinetic energies of the three types of atoms.

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Textbook Question

Oxygen (O2) has a molar mass of 32.0 32.0 g/mol. Suppose an oxygen molecule traveling at this speed bounces back and forth between opposite sides of a cubical vessel 0.100.10 m on a side. What is the average force the molecule exerts on one of the walls of the container? (Assume that the molecule's velocity is perpendicular to the two sides that it strikes.)

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Textbook Question

Oxygen (O2) has a molar mass of 32.032.0 g/mol. How many oxygen molecules traveling at this speed are necessary to produce an average pressure of 11 atm?

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Oxygen (O2) has a molar mass of 32.0 32.0 g/mol. What is the momentum of an oxygen molecule traveling at this speed?

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