# Maxwell-Boltzmann curve

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#1
does the area under a Maxwell-Boltzmann curve show the total energy of a system?
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8 years ago
#2
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#3
what does that mean?
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8 years ago
#4
(Original post by jsmith6131)
does the area under a Maxwell-Boltzmann curve show the total energy of a system?
To the left of the Ea line, it's the total number of particles that don't have enough energy to react, and to the right of it is the total number of particles that do have enough energy to react.
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8 years ago
#5
(Original post by jsmith6131)
what does that mean?
click on it
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#6
no guys just imagine a standrd curve JUST 1 with no Ea line.
The TOTAL AREA under the ENTIRE curve - does that equal the area of the system?
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8 years ago
#7
the area shows the total number of molecules.
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#8
thats is abundantly obvious from the y-axis (no of molecules) but area is base*height
so no. molecules * energy so I would presume that total area = total energy
do you agree
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8 years ago
#9
I haven't done chemistry since A level , but if a point on the Maxwell-Boltzmann curve represents the number of particles at a particular energy level, then the integral over the entire curve, that is to say the area you are describing, should represent the number of particles over all energy levels, i.e the total number of particles in the system. (I hope :P )

Further evidence for this would be that the area to the left of the Ea line represents the number of particles that don't have energy to react, and area to the right is number of particles that do have sufficient energy to react (from the definition of activation energy). Thus considering the area on both sides must be the total number of particles, since you would be adding the number of particles that cannot react, to the number of particles that can (and because this forms a partition in the system, it must be including all particles)
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#10
a little confused...are you agreeing with me or not?
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8 years ago
#11
trust me the area under the graph represents the total number of molecules present! Dont listen to these idiots.
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8 years ago
#12
(Original post by jsmith6131)
a little confused...are you agreeing with me or not?
No. To clarify, I am saying the area under the curve is the total number of molecules present in the system.
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8 years ago
#13
The Maxwell-Boltzmann distribution can be used to describe the distribution of velocities (or speeds) of the molecules as well as momentum, though it is frequently used to express the distribution of energies, as kinetic energy depends on speed.

So when you ask about what the area under the curve represents, you need to say what you are plotting on the curve.
Are you talking about a curve of the number of molecules against velocity (range) or about number of molecules in a particular energy range?
Are you referring to a probability density curve (probably) or a cumulative curve?
If you are asking about the probability density curve then the area under any portion of it is the total number (or fraction*) of molecules having that range of speeds, velocities, momenta, or energies.

http://www.chemguide.co.uk/physical/...mperature.html (scroll down)
(Or any search for "area under the Maxwell-Boltzmann curve")

* In a probability density curve the total area under the curve usually represents the total number of molecules or 100%. So a portion of the curve represents that fraction or % of the total.
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#14
no I am referring to the curve
y-axis: no. molecules
x-axis: energy
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8 years ago
#15
(Original post by jsmith6131)
does the area under a Maxwell-Boltzmann curve show the total energy of a system?
(Original post by jsmith6131)
no I am referring to the curve
y-axis: no. molecules
x-axis: energy
I'm not sure what you are answering "no" to.
If you are talking about the Maxwell-Boltzmann curve for molecular energies then
it is a so called probability density curve.
So the area under it (or any portion of it) represents the number of molecules (or rather the fraction of the total number) that have energies between the values of E on the x axis.
Mathematically, a probability density curve is not the same as a standard curve you plot like a velocity time graph. Statistical functions behave differently.

Did you look at the link I gave?
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#16
yes that was one of the sources I came across when looking for the answer
but my book had a question in it asking what does the area under the maxwell-bolztmann energy curve represent, i said "no of molecules in the system" and this was wrong
so i figured it must be something else!
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#17
btw this is for a Maxwell-Boltzmann energy distribution curve!
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5 years ago
#18
I agree completely! But everyone at physics class (including the teacher!) made fun of me for doing so. They think it is the total number of molecules.
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5 years ago
#19
(Original post by jsmith6131)
no guys just imagine a standrd curve JUST 1 with no Ea line.
The TOTAL AREA under the ENTIRE curve - does that equal the area of the system?
Yes it does according to my point of view. But the majority is against it.
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5 years ago
#20
(Original post by jsmith6131)
no I am referring to the curve
y-axis: no. molecules
x-axis: energy
To be more exact, it is------ y-axis:no. of molecules per energy, 'E'
x-axis: energy, 'E'
so the area becomes (if we consider a straight line of zero gradient):
area= energy multiplied by no of molecules/energy
= # of molecules
Q.E.D.
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