Specific heat of ammonia?

[Chatha]

After reading your posts carefully, and reading about "degrees of freedom", I believe you do have a deep understanding of this topic. However you did make a mistake of refering ammonia as NH4 instead of NH3, though I don't know for sure if this automatically affects the modes of vibration. Nontheless your assessment was flawless. So let me try to paraphrase "degrees of freedom". Vibrational nodes store energy, and the more vibrational systems you have, the more energy is absorbed. Like you said, and with reference to your first post, hydrogen bonds have very little to do with all this. Pardon my differences, you have to understand that when you are an undergrad, they tell you to always accept "ideals" without real indepth analysis. However, hydrogen bonds still have something to do with specific heat, as its another way to store energy...after V modes, though insignificant in the discussion between NH3 and H20. Water having a total maximum of 6 V modes, Librations(3) and 3 internal motions(asymetric, symetric, and bent). Ammonia probably having 2 more modes from asymetric stretch of additional atom---not sure

 

[Billy T]

... I believe you do have a deep understanding of this topic. However you did make a mistake of refering ammonia as NH4 instead of NH3, though I don't know for sure if this automatically affects the modes of vibration. ...

No, it was just a careless typo, but even if NH4 did exist, it would have the same number of rotational modes, 3, as NH3, but there would be more vibrational modes. Thanks for catching my typo.

Later by edit: -no, not a typo. I must confess I was confused. - I drew ammonia as if there were four Hs in post 5. I think my confusion was caused by recalling that it had a quadrahedron shape. Now, giving it more thought, I think the three H are in a plane and the N can be on either side of this plane. If that is correct, Amonina should be polar and some IR frequency should pump the N from one side to the other - Is this correct? I am not much of a chemist but bet NH3 is a very strong absorber for some narror band of IR.

Also thanks for reminding me that the first mode I illustrated in post 5's typed drawing is called "asymmetric stretch" and the second is the "symmetric stretch" mode. I should have given those standard names.

As I may not get back here and I like to teach I will tell you why N2 and O2 have only 2 rotational degrees of freedom and confess that I spoke of them as symmetric molecules with no permanent polarization mainly to help you guess foolishly that the fact they are un-polarized might have something to do with it. It does not. CO is a permanently polarized molecule (the O end being more negative) and also has only 2 rotational modes. It has to do with the fact that the energy levels are quantized and in the classical analogy of a rotator, the energy is (1/2)I w^2 (w is usually written as the Greek omega, but I forget how to do that here.) Thus if I, the moment of inertia about one axis of the rotation, is very small then the angular rate, w, must be very great to have the energy of the first excited state. Hence in a collisions it is essentially impossible to spin any linear (diatomic) molecule about the axis passing thru the two atoms fast enough*. Since no energy can excite even the first excited state about this axis it is as if this rotational mode did not exist.

In contrast almost any molecule with three or more atoms will have a non- zero I about all three axises, so all three can store energy. Perhaps there are some co-linear three atom molecules, but not with oxygen as the central atom as no pair of the oxygen "orbitals," where atoms can bind, are 180 degrees from one another. Lynis Pauling (only winner of two Noble Prizes on different areas) got one for his work on these "orbitals." - I think he wrote a book, "The nature of the chemical bond" which discusses all this if you want to know much more than I do.

It is always good to question what you are taught, but give your professors the benefit of the doubt when you simply do not understand.
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*Sort of like trying to spin a very small diameter steel rod about its axis by hitting it. - Nearly impossible, but easy to make it tumble about either of two axis which are orthogonal to the rod’s axis.

 

[Billy T]

Basically, what I understand is that there are three translational motions, as in the 3 dimensions of space particles can move; X,Y,Z. Then there are other internal motions refered to as rotational or internal motions, which all store energy. The more degrees of freem a substance has, the higher the specific heat because the more nodes to store energy. Mono atomic substances have only 3; translational, thus they have the lowest SHC. Many molecules have 5 degrees, which is why they have 5/3 the SNC of their mono-atomic references. My guess is that the internal degrees of freedom comes from the inertia/angular momentum of collision with other atoms, but I may be wrong. What's your opinion?

Mostly correct. You are learning, and that makes me feel good, if I am partly why.

Many of the most common molecular gasses are dia atomic and thus effectively have only two rotational modes. Hence the 5 degrees of freedom. Typically the rotational energy levels are much closer to the ground state and thus easier to excit. Here your earlier concern about the strength of the bond does have some validity. The strong bond and light weight of hydrogen does make the first excited vibrational state more widely separated from the ground state. (Sort of like a stiff spring and light weight has a higher frequency of vibration than a soft spring and/ or heavy weight. Crudely speaking, the higher the lowest quantized mode of vibrations frequency is, the greater is the energy needed to excite it and the less likely it is to store any added energy. Thus, the effect of the strong H bond is just the opposite of what you were thinking.)

I.e. at room temperatures the added energy goes mainly into translation and rotation, not vibration but to fully understand this you will need to learn about the statically distribution of energy (in thermal equilibrium) among the various possible energy level states. lets not go into that now.

From what you have already learn, you can now understand why CO2 and H2O are so important in the "green house” gases despite being only a very small fraction of the atmosphere (but much more of the story is related to fact that both are polar molecules and thus can interact with electromagnetic radiation, especially IR and non-polar O2 and N2 can not easily interact with IR radiation.)

 

[Chatha]

http://www.ems.psu.edu/~bannon/moledyn.html
http://www.pha.jhu.edu/~broholm/l37/node5.html#SECTION00011030000000000000
The one place I am confused is why diatomic molecules have 2 rotational energy. My guess is that the third unexcited axis has to do with low angular rate, since linear molecules are 180 degrees. Like you said, its almost impossible to make a micro diameter rod spin by simply hitting it. It seems to me that the Inertia or angular momentum needed for the x axis is inefficient, but from the visual references I posted. I can't really understand. I understand all the basics but I just can't put it together. But the one thing I can understand is that NH3 must have more derees of freedom since it has more atoms. Thanks for the advice.

 

[Chatha]

For me, the best way to begin to understand degrees of freedom is, s= C/(R/2), where R is the gas constant, C is the specific heat under constant pressure @25 degrees celcius, and s is the degrees of freedom for the molecule. Solving the equation I got 18 for water, which means each aton has 6 degrees of freedom. I got 19 for ammonia, which means each atom has 5 degrees of freedom. I can also see why degree of freedom is probably more important than Hydrogen bonds or molar mass.