# Why are specific heat high in water but low in ethylene glycol?

1. Aug 13, 2012

### junglefish1

Im sorry to ask such a question but Ive been trying to understand the molecular reasons for why specific heat is high in some molecules but low in others. For example water has a specific heat of 4180 yet has a boiling point of 100 degrees Celsius but ethylene glycol (ethane 1,2 di-ol) has a boiling point of 194 degrees Celsius yet it has a specific heat of around 2200, so because of this it cant be due to bonds because you would think that if the bonds were the reason then ethylene glycol would have a specific heat due to its strong bonds. So then I found that its due to the amount of energy which they store, the degrees of freedom. Where there is 3 translational, 2 or 3 rotational depending whether the molecule is linear or non linear, thus the amount of degree of freedoms for vibration is 3N-5 or 6. But when that is found it gives larger molecules a larger number of degrees of freedom then smaller ones such as H20 or H2 which both have very high specific heat (especially H2 which is around 14.26 from memory) Anyways, my question is what am I missing basically? How come water has less way to store energy then ethylene glycol yet has a high specific heat?

Thanks to anyone that have time to spare to explain this, much appreciated as I have spent a while reading internet pages and both physics and chemistry textbooks without prevail. Cheers

Last edited: Aug 13, 2012
2. Aug 13, 2012

### Simon Bridge

Welcome to PF;

You have related two models that depend on the complexity and mass of the molecules as well as on inter-molecular forces. Let's see if I've understood you:

Temperature is related to the mean kinetic energy per molecule.

The bp is the temperature where the speed of the molecules is enough to break free from the intermolecular forces keeping the substance a liquid. The molecules that have broken free have "changed state".

Specific heat capacity is the amount of energy you need to give the substance as a whole to raise it's temperature.

A given amount of heat supplied to a substance gets divided between the different degrees of freedom available to each molecule as well as other features of the chemistry of the substance.

You expect more complex (measured by number of degrees of freedom) molecules to lead to a smaller proportion of heat to be available to translation and so lower speeds. So it requires more energy to get the molecules up to phase-change speeds, and more energy to raise the temperature, than for simpler molecules. Means higher bp would go hand-in-hand with higher heat capacity.

Since this is not always the case, you can conclude that something else is going on and/or the details of the relationships are more complicated than suggested by this simple qualitative analysis.

You want to know what those differences are in the case of water and ethylene glycol.
Would this be correct?

Compare, in general:
Specific Heats and boiling points of common liquids with their general complexity (as measured by number of degrees of freedom) - A complex substance does not have to have a higher bp than a simple one for eg. Methanol is a liquid at room temperature, many more degrees of freedom than water, yet less than half the boiling point.

The more atoms you have more per molecule the worse the model becomes.
On top of that, as well as Van der Waals type inter-molecular forces you also have to deal with the possibility of chemical reactions at different temperatures, and quantum effects.

For a starting point see:
http://en.wikipedia.org/wiki/Heat_capacity#Theory_of_heat_capacity
... discusses the relationship between DoF and C and where other effects may come in.

So you need to compare more similar substances:
methanol bp 66C hc 2.47-2.51 kJ/kgK CH3OH
ethanol bp 78C hc 2.3-2.7 kJ/kgK C2H5OH

Methanol has fewer degrees of freedom than ethanol and a lower boiling point - but it's specific heat is slightly higher at room temperature ... only at higher temperatures does the expected, rule of thumb, relationship appear.

The underpinnings of material properties - especially when you want to account for specific values of properties of specific substances, is very complex and huge books get written about it.

3. Aug 13, 2012

### junglefish1

Hah thankyou yeah ive realised that the provide a theoretical explanation for why some molecules contain higher specific heats the others its rather complex and Im sure if I right but it can be impossible at times? Well without experimentation.

But since Ive been researching this for the past week I think Im finally understanding why water for example has a really high specific heat, which is not only due to its degrees of freedom and the amount of atoms per gram (can hold more heat per gram) but due to its hydrogens bonds the different kinetic movements such as vibrational, translational and rotational all require more energy due to the fact that they have account for the strong attraction forces between molecules and within the intermolecular forces as well. Is that right?

Which would also explain ammonia also has an usually high specific heat. It can the be related to ethylene glycol to which yes I am comparing between water. Ethylene glycol does have those hydrogen bonds but they aren't as strong with it as it is within water and ammonia. IS that right?

And just so Im understand the equipartition of energy right, is states that all degree of freedom have the same energy thus the energy is distributed evenly amongst them. Is that right?

Sorry about asking so many questions just trying to clarify my thoughts of this topic. Haha but thanks for your help so far, hahaa its help me gets my thoughts organised a bit better which makes more sense. Haha and yeah ive read that wikepedia link around 6 times, but each time I do i seem to understand a bit more about it which is good haha, thanks heaps :)

4. Aug 13, 2012

### Simon Bridge

Oh yes - the molecular density is also important.
You'll see that heat capacity is a bulk thing while the phase change tends to depend more on what an individual molecule is doing.

Water, you will find, is a special case for quite a large number of things. It's not usually very good for working out general rules that apply to other molecules.

For one thing, H2O has a bend in it. This gives it 3 ways to rotate and an extra way to vibrate (each H can vibrate along the bond, and the whole molecule is more flexy).

http://en.wikipedia.org/wiki/Triatomic_molecule

The O-H bond in liquid water is not known to be particularly strong. A glass of water at room temp typically contains an equilibrium of H2O, HO- and H+ ... an excess of OH- makes a solution alkaline and an excess of H+ makes it acidic, so water is neutral. A glass of pure H2O would be "100% de-ionized water" and it doesn't stay that way long.

Part of the odd properties of water is that the O-H bond is polar - the H end is slightly positive and the O end slightly negative. The kink in it means the negative part is more exposed than for a linear molecule ... the whole molecule is slightly polar. The geometry affects how ice crystals form and, of course, strengthens the inter-molecular forces.

In e-glycol there are H-C H-O and C-C bonds.
C-C bonds are strong in some configurations (eg diamond) and weak in others (eg graphite). To complicate matters, one of the H ends is weakly attracted to the opposite O.

Ammonia NH3 has the N in a triangle of H's ... if you put a z axis through the middle of the triangle, perpendicular to it's plane, the N oscillates (iirc) along that axis. Again, H is a good donor, so the three H ends are slightly positive. Ammonia is another odd substance.

Basically, H O N and C are each funny beasties which make these odd-behavior molecules which resist general rules of thumb ... so naturally they are essential for life. :)
These are actually the four most common elements in the human body.
http://en.wikipedia.org/wiki/Composition_of_the_human_body
... i.e. do not expect easy-to-understand behavior from their molecules.

Vibration and energy:
What you are noticing is that the vibrational and rotational modes are quantized - the weaker the bond, the closer together the (vibrational) energy levels. $E_n=(n+\frac{1}{2})\hbar\omega$ ... the tighter the bond the bigger $\omega$. This also means it takes more energy to add to the vibration.

Equipartition of energy:
In classical thermodynamics, thermal energy is distributed evenly between each degree of freedom. As you've seen, the quantum mechanics is trickier. This is why head capacity is temperature dependent and why the books keep using the hand-wavey "quantum effects" to avoid talking about it.

Last edited: Aug 13, 2012
5. Aug 14, 2012

### junglefish1

hahaha i just had my breakthrough with the vibrational energy and the bond strength thanks to your equation and your link about the vibrational of triatomic molecules!okay so basically:
En = (n+1/2)hw where 'w' is the frequency of the vibrations. As seen on: http://en.wikipedia.org/wiki/Triatomic_molecule

There are three different ways a triamotic molecule can vibrate which is directly proportional to the spring constants of the molecule which is directly proportional to the strength of the bond. Because the stronger the bond the stronger the more the object will spring, thus the higher the frequency and as seen in the equation above, the more energy.

Haha thankyou so much, Ive been trying to figure a reason why the strength of a molecule increases the vibrationals energy for like a week and being one of those people that have to understand 'why' something happens, I cant write my report without first understanding everything behind it. Thanks heaps and basically Im just going to use this as a factor involving the increase in specific heat, as specific heat is related to lots of other factors aswell which i dont have time to find them all nor the intelligence probably either haha im guessing it would go into like material engineering and so on... so thanks heaps you saved me big time.

6. Aug 14, 2012

### Simon Bridge

Well if you understand the subject to greater depth than you need the report will be stronger. Sometimes though, you just have to jump in the water and take the consequences - one of the beauties of physics is that you can very quickly get to a place where nobody understands everything about a topic and you still have to cope.