Uranium has two naturally occurring isotopes. has a natural abundance of and has an abundance of . It is the rarer that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, , which is a gas, then allowing it to diffuse through a series of porous membranes. has a slightly larger rms speed than and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of to that of
Root mean square velocity of is.
The average translational kinetic energy is
The molecule with massand velocity has an average translational kinetic energy,
Equating equationandhave the same left side,
Root mean square velocity is,
The root square of the molar mass is inversely proportional to root mean square velocity.
The molar mass of fluorineis.
So, the molar mass of is,is.
The two containers of gas in FIGURE Q20.8 are in good thermal
contact with each other but well insulated from the environment. They
have been in contact for a long time and are in thermal equilibrium.
a. Is vrms of helium greater than, less than, or equal to vrms of
b. Does the helium have more thermal energy, less thermal
energy, or the same amount of thermal energy as the argon?
At what temperature does thespeed of a nitrogen molecule and a hydrogen molecule equal the escape speed from the earth's surface? You'll find that these temperatures are very high, so you might think that the earth's gravity could easily contain both gases. But not all molecules move with . There is a distribution of speeds, and a small percentage of molecules have speeds several times . Bit by bit, a gas can slowly leak out of the atmosphere as its fastest molecules escape. A reasonable rule of thumb is that the earth's gravity can contain a gas only if the average translational kinetic energy per molecule is less than of the kinetic energy needed to escape. Use this rule to show why the earth's atmosphere contains nitrogen but not hydrogen, even though hydrogen is the most abundant element in the universe.
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