Ball Lightning: Uncovering the Mystery of N_7^{14}, H_1^1, & O_8^{16}

[Karol]

Homework Statement

Ball lightning is a sphere shaped lightning that stays long before it explodes. they are sometimes created in a lightning storm.
The theory says they are made of nitrogen ions surrounded by water molecules. the temp' inside is 600⁰C and outside 20⁰C.
Nitrogen: $N_7^{14}$ Hydrogen: $H_1^1$ Oxygen: $O_8^{16}$
The atmosphere consists of 80% N₂ and O₂
How many molecules of water, in average, surround each nitrogen ion.

Homework Equations

$$0^0c=273^0K$$
The equation of state: $PV=nRT$

The Attempt at a Solution

i don't know even which discipline is that problem, is it thermodynamics? chemistry?
Please give a direction to start, at least

 

[Drakkith]

i don't know even which discipline is that problem, is it thermodynamics? chemistry?

What class or book is this problem from?

 

[Karol]

I don't know which book it was taken from, i received it from a pupil.

 

[Drakkith]

It looks like chemistry to me, but I really don't know.

 

[haruspex]

Complete guess here, but...
Consider a ball of lightning and a ball of air of the same volume. What else must be about the same for them? What does that tell you about the ratio of moles?
(Note that this approach requires you to assume the other gases present in air do not much alter its density.)

 

[andrevdh]

I tend to agree with you.
The lightning ball is a relatively stable structure, so I would think one should just treat it as a ball of hot air floating in a cooler atmosphere.
Somehow the eletrostatic forces keep it from expanding in spite of its high temperature.

 

[haruspex]

Somehow the eletrostatic forces keep it from expanding in spite of its high temperature.

No, you must not assume that, or you will not have enough information!
Ask instead why should it expand.

 

[Karol]

Complete guess here, but...Consider a ball of lightning and a ball of air of the same volume. What else must be about the same for them? What does that tell you about the ratio of moles?
(Note that this approach requires you to assume the other gases present in air do not much alter its density.)

The pressure in the ball is one atmosphere also, so pv=const.
The masses in the ball and the ratios of gases is the same as $20^0$ air, only the arrangement has changed:
$$1[mol]_{air}=0.8[mol]_{N_2}+0.2[mol]_{O_2}=1.6[mol]_N+0.4[mol]_O$$
$$\rightarrow~~x=\frac{1}{4}$$
On every 4 ions of N there is 1 molecule of water

 

[nasu]

O₂ is not water. If it's the same as dry air, where does the water comes from?
The formulation "The atmosphere consists of 80% N2 and O2" is confusing".
Is there a typo (meaning actually "and 20% O2) or in these special conditions, the nitrogen and oxygen are just 80% (together)?
There is no indication about content of water or where the water comes from.

 

[haruspex]

The pressure in the ball is one atmosphere also, so pv=const.
The masses in the ball and the ratios of gases is the same as $20^0$ air, only the arrangement has changed:
$$1[mol]_{air}=0.8[mol]_{N_2}+0.2[mol]_{O_2}=1.6[mol]_N+0.4[mol]_O$$
$$\rightarrow~~x=\frac{1}{4}$$
On every 4 ions of N there is 1 molecule of water

I don't understand how you got that. I find there are several water molecules per N. Please post your working.

 

[andrevdh]

So it would not be soluable if one were to use just Archimede's principle?

 

[haruspex]

So it would not be soluable if one were to use just Archimede's principle?

Well, not just Archimedes' principle. You have to use a few other things too.

 

[andrevdh]

I think the op should state his/her assumptions first.

 

[haruspex]

The masses in the ball and the ratios of gases is the same as 20^o air, only the arrangement has changed:

Not sure what you mean by that. The ball consists of nitrogen ions with clusters of (ionised?) water molecules around them. No air. But it has the same density as air, or it would not float, and the same pressure, as we are assuming there's no strong electrostatic force to contain it or to dispel it.

 

[andrevdh]

Ok. Got it now.

 

[Karol]

Air at 20⁰:
$$PV=nRT~~\rightarrow~~100,000=n\cdot 8.31\cdot 293~~\rightarrow~~n=41.1[mol]$$
I chose pressure of one atmosphere and volume of one metre cube.
Ball thunder:
$$n=\frac{293}{873}41.1=13.8[Mol]$$
But if the density of the ball must be the same as air at $20^0$:
$$2(0.8\cdot 14+0.2\cdot 16)=28.8[gr/mole]$$
$$\rho=\frac{28.8\cdot 41.1}{1}=1,183.7[gr/m^3]$$
Then we didn't do anything, and it also can't be since we must use the equation of state.

 

[haruspex]

If there are k water molecules/ions attached to each nitrogen ion, what is the molecular weight of the cluster? What density does that give at the known temperature and pressure?

 

[Karol]

The ion of nitrogen is one atom. The unit in the mol of the ball is the cluster of the nitrogen atom plus the water molecules.
In post #16 i found the density of the air at 20⁰ to be 1183.7 and that there are 13.8 moles in the ball.
The density remains the same and it is made of clusters:
$$\rho=1,183.7=[k(16+2)+14][\frac {gr}{mol}]\cdot 13.8[Mol]~~\rightarrow ~~k=4$$

 

[haruspex]

The ion of nitrogen is one atom. The unit in the mol of the ball is the cluster of the nitrogen atom plus the water molecules.
In post #16 i found the density of the air at 20⁰ to be 1183.7 and that there are 13.8 moles in the ball.
The density remains the same and it is made of clusters:
$$\rho=1,183.7=[k(16+2)+14][\frac {gr}{mol}]\cdot 13.8[Mol]~~\rightarrow ~~k=4$$

Yes,that's fine, but in post #8 you wrote

On every 4 ions of N there is 1 molecule of water

I guess you just got it backwards when posting.

 

[Karol]

I didn't see post #8 when I wrote the last one. It is just accidentally the same number 4. Now there are 4 water molecules on every nitrogen atom.

 

[haruspex]

I didn't see post #8 when I wrote the last one. It is just accidentally the same number 4. Now there are 4 water molecules on every nitrogen atom.

Ok. From memory, I got 4.5. It asks for an average, so need not be an integer.

 

[Karol]

Maybe you didn't take into account the hydrogen. I also got 4.5 in this case. Thank you haruspex.