10/14/2014
ALEKS Alex H. Yuan - 10/14/2014 11:18:25 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Alex H. Yuan - 10/14/2014 11:18:25 PM EDT
General Chemistry (First Semester) / Chem 110 FA 2014 – CH110 FA14 S25-36 (Dr.
Barber)
1.
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10/14/2014
ALEKS Alex H. Yuan - 10/14/2014 11:18:25 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Interpreting a graph of molecular speed distribution
Here is a graph of the probability of an atom moving with a particular speed, for a
sample of helium gas at
y
probability
x
0
500
1000
1500
2000
2500
3000
speed (m/s)
Use this graph to answer the following questions. Round each of your answers to the
nearest
Note: your answers must be within
correct.
What is the most likely speed of a
of the exact answers to be graded
atom in this sample?
What higher speed is only half as likely as the most likely speed?
What higher speed is only
as likely as the most likely speed?
Since this question asks about the motion of the atoms or molecules in a gas, it must be a
question about the kinetic theory of gases.
The key idea you'll need from the kinetic theory of gases is that the atoms or molecules in a
gas don't all move at the same speed. At any given moment some molecules are moving
faster, and some are moving slower.
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10/14/2014
ALEKS Alex H. Yuan - 10/14/2014 11:18:25 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Furthermore, not all speeds are equally likely. Both very low and very high speeds are quite
unlikely. The most likely speeds cluster around a medium value determined by the
temperature of the gas and the mass of the atoms or molecules in the gas.
The exact distribution of speeds of atoms or molecules in a gas is given by the MaxwellBoltzmann distribution, which is what's graphed in the question. This distribution tells you
the probability that an atom selected at random will have a particular speed.
For example, if the Maxwell-Boltzmann distribution of a particular gas were
a speed of
you would know there's an
selected at random from this gas will be traveling at
students: more precisely, there's an
of
at
chance that an atom
(Note for advanced
chance the speed will be within
)
Now let's apply these general ideas to solve the problems you've got.
The most likely speed of atom in this sample is the speed where the MaxwellBoltzmann distribution reaches its highest value. By looking at the graph, you can see
that is
in this case.
The higher speed half as likely as the most likely speed is where the MaxwellBoltzmann distribution falls to half of its highest value. That turns out to be
in this case.
The higher speed only
as likely as the most likely speed is where the MaxwellBoltzmann distribution falls to one tenth of its highest value. That turns out to be
in this case.
Here is the completed table:
What is the most likely speed of a
atom in this sample?
What higher speed is only half as likely as the most likely speed?
What higher speed is only
as likely as the most likely speed?
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10/14/2014
ALEKS Alex H. Yuan - 10/14/2014 11:18:25 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Copyright © 2014 UC Regents and ALEKS Corporation
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