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Solved: Helium (He) is the lightest noble gas component of
Chapter 5, Problem 5.76(choose chapter or problem)
Helium (He) is the lightest noble gas component of air, and xenon (Xe) is the heaviest. [For this problem, use R 8.314 J/(mol K) and in kg/mol.]
(a) Find the rms speed of He in winter (0. C) and in summer (30. C).
(b) Compare the rms speed of He with that of Xe at 30. C.
(c) Find the average kinetic energy per mole of He and of Xe at 30. C.
(d) Find the average kinetic energy per molecule of He at 30. C.
Questions & Answers
QUESTION:
Helium (He) is the lightest noble gas component of air, and xenon (Xe) is the heaviest. [For this problem, use R 8.314 J/(mol K) and in kg/mol.]
(a) Find the rms speed of He in winter (0. C) and in summer (30. C).
(b) Compare the rms speed of He with that of Xe at 30. C.
(c) Find the average kinetic energy per mole of He and of Xe at 30. C.
(d) Find the average kinetic energy per molecule of He at 30. C.
ANSWER:Step 1 of 10
a)
In this exercise, we must determine the root-mean-square speed of helium in \(0^{\circ} \mathrm{C}\) and \(30^{\circ} \mathrm{C}\).
The molar mass of helium in kg/mol can be given as:
\(M_{\mathrm{He}}=4.003\times10^{-3}\mathrm{\ kg}/\mathrm{mol}\)
The temperatures of interest in kelvins can be given as:
\(\begin{array}{l}T_1=0^{\circ}\mathrm{C}=273\mathrm{\ K}\\ T_1=30^{\circ}\mathrm{C}=303\mathrm{\ K}\end{array}\)
Before solving the exercise, let's discuss the main principles.
Kinetic energy is an energy value associated with the motion of an object, say those of particles. The magnitude of kinetic energy depends on the mass and the speed of an object.
\(E_{k}=\frac{1}{2} m \times u^{2} \ldots\ldots(1)\)