# Homework Help: What prevents molecules from being too close to each other?

1. Jan 29, 2013

### sgstudent

1. The problem statement, all variables and given/known data
When we have a liquid, there are Van der Waals forces of attraction in between each molecule. Hence, the negatively charged electron cloud would be attracted to the positive nucleus of the neighboring molecule. However, there seems to be a gap in between the molecule (least in the solid and the most in the gas). Why is this so?

2. Relevant equations

3. The attempt at a solution
From this link: http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/waal.html it seems to me that the heat the molecules have prevents them from colliding to each other. So if the general formula for it would be initial KE+work done against attraction=final KE then it seems that temperature should decrease. However, that is not the case and the attraction should be an internal energy too (similar to gravity i think?). So I am still confused on how heat prevents the molecules from moving to close to each other.

Thanks for the help

2. Jan 29, 2013

### ehild

The electron clouds repel each other. Remember that the positive nucleus is very small with respect to the size of an atom, so when two atoms approach each other, the repulsion between electrons overrides attraction to the nucleus. This repulsion makes the atoms/molecules behave as balls in an elastic collision.

Because of the high speed of the particles, they spend very short time in the vicinity of each other, so their interaction can be ignored if the temperature is high enough. Also, the density is low and the molecules occupy very small volume with respect to the volume of the vessel: two particles get close to each other with law probability.

ehild

Last edited: Jan 29, 2013
3. Jan 29, 2013

### sgstudent

Hi thanks for the reply. But how will the attraction be overridden by the repulsion? Since the nucleus will always be closer to the electron cloud of the other molecule than the other electron cloud. Something like this: http://postimage.org/image/5udw1tubf/ [Broken] but actually thinking deeper why won't the 2 positive nucleus repel each other and the 2 negative electron clouds repel each other cancelling any attraction? Somehow i suddenly thought of this which also doesn't make sense in the real world.

Also, how would temperature allow the particle to move further from each other? was my formula initial KE+work done against attraction=final KE correct? I don't think so as the attraction should be an internal force. So I'm still quite confused about how heat allows the particle to move away.

Thanks ehild

Last edited by a moderator: May 6, 2017
4. Jan 29, 2013

### ehild

The nucleus of an atoms is much-much smaller than the atom itself, even than the radius of the innermost electron orbit.

http://en.wikipedia.org/wiki/Atomic_nucleus. You can imagine a hydrogen atom like in he picture. Your drawing shows dipole molecules, where the electron cloud has the shape so one part of the molecule is more positive, the other side is more negative. You see when the atoms get close it is their electron clouds closest than the nuclei. You know from Coulomb's Law that the the force between two charges is inversely proportional to the square of the distance between them.

If the atoms are far away, the repulsion and attraction cancel, just as you wrote. The atoms of a common gas do not interact most of the time. But they can get close accidentally, and then they interact. This interaction depends on the distance. They can attract each other from moderate distance, by distorting the electron clouds, so the atoms behave as dipoles as in your picture. But it is repulsion at short distance: The atoms can not penetrate into each other only at very high energies. Very close to an atom, it is a repulsive force field.

Having some KE, it decreases because of the work of repulsive force in that field, and the particle stops at a certain distance. Because of the repulsive force, it will accelerate away, and it gets back its initial KE at the end.

ehild

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5. Jan 29, 2013

### sgstudent

Thanks for the reply :)

Oh, so when the molecules of a gas are very close to each other they will repel each other while if they are moderately close to each other they will attract. Is this the same for liquids? Such that as they go too close to each other they repel and as they go further they attract.

But actually what i meant by cancelling out was this: http://postimage.org/image/ay2mxebrn/ [Broken] i thought of this. But it seem unreal as in more general experiments where there are 2 polarized objects would still attract. But looking at the Coloumb's Law, the distance might cause the attraction to be stronger than the repulsion. In this image I will show my rough working: http://postimage.org/image/72hselwyb/ [Broken] I didn't use the constants but this is a rough estimation. Would this be a good enough reason for the attraction? The same formula would work when the particles are very close to each other (so overall repulsion).

Thanks for letting me know about Coloumb's Law it solved a lot of questions that went on in my mind for a while :)

But then again, how does heat factor in? As we increase the temperature and let it stabilize at that temperature, why would the particles move further from each other?

Thanks ehild, you were great with the explanations

Last edited by a moderator: May 6, 2017
6. Jan 29, 2013

### ehild

In your drawing, both electrons are at the right side of their atoms. It is not so. You can imagine the electrons orbiting around the atom very fast, so you can just observe an electron cloud. The electron can be anywhere along its orbit. So those atoms in the picture can have the two electrons at distance 1 from each other with the same probability of being at distance 4. And when they are very close, the repulsion force is very strong. Try to calculate with half electrons at both sides of an atom. :)

You will learn that temperature is connected to the kinetic energy of the molecules. When you heat up a substance, you increase the kinetic energy of its particles.
In case of a gas, the average distance of the molecules is determined by the vessel and the number of the molecules.
In a liquid or solid, the position of the molecules are determined by the attractive and repulsive forces. Their stable position is there where these forces cancel. But they still have kinetic energy, so they oscillate around the stable position, like two balls, connected to the ends of a spring. The total energy is constant, and farther from equilibrium, KE transforms to potential energy. At maximum distance from equilibrium, the KE is zero, and we call that distance amplitude. You know, the higher the energy of the oscillating body, the greater the amplitude, the farther apart can the balls (atoms, molecules) reach away from each other. You will learn, that the potential energy is not symmetric: it is easier to get away than to get close: In average, a liquid or solid usually extends at higher temperature.

All these explanations are oversimplified, as I do not know what you have learnt so far. (There is an other important effect that contributes to repulsion: That the electrons can not be in the same states. It is called Pauli's Exclusion principle. http://en.wikipedia.org/wiki/Pauli_exclusion_principle, I did not talk about).

As you study Physics, you will learn and understand more and more about the behaviour of atoms and molecules, but we never will understand them fully.

ehild

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7. Jan 29, 2013

### sgstudent

Hi :) the electrons can be anywhere but i thought when they are at a distance they would attract each other? And only when they are close to each other then they would repel each other?

Oh so as we increase the KE the PE will also increase. But are they considered separate as in this http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html#c1 is seems that the potential energy component is different from the kinetic energy. They mention that some heat is used to increase the potential energy component. What does that mean?

8. Jan 29, 2013

### ehild

Electrons all have the same negative charge, they always repel each other.

The link speaks about phase change. That happens when the temperature is so high that the particles gain KE big enough to escape from their potential well.
You can not say that the heat added to a substance increases the PE or the KE.
Heating a substance means to increase its internal energy, that is the energy of the random motion of its particles.
Potential energy and kinetic energy are connected, and their sum is constant. Like in case of ball on a string (simple harmonic motion). At the equilibrium position, the particle has only maximum KE and minimum PE. Farthest from the equilibrium position, the potential energy is maximum and the KE is zero. If you increase the kinetic energy, the particle can move farther from equilibrium, so can have higher potential energy.

The molecules of liquids and solids vibrate about their equilibrium position. They have both PE and KE.

The molecules of a gas move randomly in the vessel, that is translational motion. They can also rotate. At ordinary temperatures, the particles of a gas do these two kinds of motion. Only if they get very close to each other, experience they some force from each other, and some of their KE transforms into PE.

ehild

9. Jan 29, 2013

### sgstudent

I'm sorry but i don't really understand how the electron cloud would interact with the other neighboring atom. if the 2 electron clouds face each other, then the 2 atoms would repel and move away from each other however, isn't there a possibility that the electron cloud is facing the other direction like in my image?

Sorry the link was wrong the link should be the "Details of Heating Water" part whereby they stated: It is known that 100 calories of energy must be added to raise the temperature of one gram of water from 0° to 100°C. Part of that energy increases the kinetic energy of the molecules, and some adds to the potential energy.

Oh i think i get it. By having more heat there is more kinetic energy thus allowing the work done against attraction/repulsion or the gain/loss in potential energy more. So if i apply the work-energy theorem the formula would just be like this KE=PE as there are no work done by external forces because the attraction and repulsion are considered internal forces?

Also, when heat is conducted the particles would vibrate and knock onto the neighboring particle thus increasing it's kinetic energy.

10. Jan 29, 2013

### ehild

The electron cloud is around the positive nucleus, so the electron clouds "meet" when two atoms or molecules collide.

The heat added increases the energy of the molecules. In a fluid, they are vibrating and they have both kinetic energy and potential energy, and those energies transform into each other during the vibration.

Yes, something like that happens.

ehild

11. Jan 29, 2013

### sgstudent

Oh thanks so much for the help

So during heating KE increases so the total internal energy increases. However, what did you mean by "That happens when the temperature is so high that the particles gain KE big enough to escape from their potential well. "

Thanks :)

12. Jan 30, 2013

### ehild

The attractive forces between molecules of a gas are of dipole origin at moderate distances. When the molecules are very close, so the atoms "touch", the atoms behave like solid balls with certain radii. You can read those van der Waals radii in the Periodic Table. The atoms feel high repulsive force for distances shorter than the sum of their radii. I tried to explain it with Coulomb force, but it is rather connected to Pauli's exclusion principle, explained in Quantum Mechanics. The essence is that electrons just hate each other Do not worry about it before studying Quantum Mechanics. (Anyway, if you tried to bring two electrons together, they would repel each other with their Coulomb force.)

The potential energy depends on he separation between the particles, and it is minimum at equilibrium. (See picture.) The curve is called "potential well". The minimum energy is -EB, where EB is the binding energy. The potential function goes to infinity at shorter distances and tends to zero with increasing distance. Giving EB energy to the molecule, the constituents separate, escape from the "potential well". That happens during a phase change. When water evaporates, the water molecules escape from their potential well which keeps them in the water phase and become free to move as particles of the vapour.

You can read more here, http://www.insula.com.au/physics/1250/L6.html

ehild

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13. Jan 30, 2013

### sgstudent

Oh thanks again :)

I found this link http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/inteng.html under the Internal Energy Example part which contradicts the concept of the KE and PE being under the same total internal energy (meaning the maximum KE is equal to the maximum PE). They seem to associate the 2 completely differently whereby KE is one thing and PE is another?

14. Jan 30, 2013

### ehild

Maximum KE=maximum PE is valid for vibrations. The molecules of solids and liquids can only vibrate around their equilibrium positions.

The molecules of a gas can translate and rotate, having translational and rotational kinetic energy.
No potential energy is involved unless they get very close to each other.

The atoms of a molecule can also vibrate, and for that kind of motion it is true the the maximum vibrational KE is equal to the maximum potential energy.

ehild

15. Jan 30, 2013

### sgstudent

Oh but what does this mean "When the sample of water and copper are both heated by 1°C, the addition to the kinetic energy is the same, since that is what temperature measures. But to achieve this increase for water, a much larger proportional energy must be added to the potential energy portion of the internal energy."?

Because in this case they seem to associate potential energy as completely different from kinetic energy while shouldn't they be the same thing since max KE=max PE?

16. Jan 30, 2013

### ehild

That has no sense.

Increase of the temperature is related to the increase of the average energy per degrees of freedom according to the Equipartition Principle: in thermal equilibrium, there is (1/2) κT energy for each degrees of freedom. Three degrees of freedom is associated to translation, 2 for rotation of a diatomic molecule, three for the rotation of a molecule with 3 or more atoms.
When the atoms in a molecule vibrate, there are vibrational degrees of freedom, and two belongs to each kind of vibration. But that degrees of freedom are exited only at high temperatures.
The constituents of a solid or liquid can vibrate, and have two degrees of freedom for each kind of vibration.
If you have N molecules, and there are f degrees of freedom per molecule, E=(1/2)κT f N heat energy is needed to increase the temperature by 1°.

Water is special, as the water molecules are connected through weak hydrogen bonds. The vibrations of these bonds are easy to excite, so the vibrational freedoms are alive at room temperature, and they are many. To increase the temperature by 1° , 1/2 κT has to be given to all degrees of freedom per molecule.

I suggest to start some systematic study. You are very much interested in the properties of matter, but you can understand it if you start from the beginning. Read about Kinetic Theory from a good book.

ehild

17. Jan 30, 2013

### sgstudent

Thanks for the reply

Okay! Yeah i agree with the systematic learning part seems like I still don't understand much about the main ideas and concept. Learning only the basic UK 'O' levels syllabus creates a lot of misconceptions when asking myself this kind of question. Do you recommend any book to start with that is one level above what I've learned?

18. Jan 30, 2013

### ehild

Sorry, I live in Hungary and I do not know what you really learnt. As for General Physics, I know Halliday, Resnick, Walker : Fundamentals of Physics, which is good. Chapter 19 discusses the kinetic theory of gases.
Have you studied Calculus? Ask your question at the forum General Physics, there are a lot of people here who can suggest books to you.

ehild

19. Jan 30, 2013

### sgstudent

Okay. Thanks again ehild I'll post this post on the forums to let them know where I can get a book that caters for my level. Thanks :)

20. Jan 30, 2013

### ehild

Can try also
"Introductory Physics Learning Materials " here.

ehild

21. Jan 30, 2013

### sgstudent

Re: Re: What prevents molecules from being too close to each other?

Hi ehild I can't post any topics on that forum. It seems to be disabled for me?

22. Jan 30, 2013

### ehild

It can be. But you can see the material there.

ehild