# Homework Help: Ball lightning

1. Jul 25, 2016

### Karol

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
$$0^0c=273^0K$$
The equation of state: $PV=nRT$

3. 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

2. Jul 25, 2016

### Staff: Mentor

What class or book is this problem from?

3. Jul 26, 2016

### Karol

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

4. Jul 26, 2016

### Staff: Mentor

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

5. Jul 26, 2016

### 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.)

6. Jul 27, 2016

### 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.

7. Jul 27, 2016

### haruspex

No, you must not assume that, or you will not have enough information!

8. Jul 28, 2016

### Karol

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

9. Jul 28, 2016

### 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.

10. Jul 28, 2016

### haruspex

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

11. Jul 29, 2016

### andrevdh

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

12. Jul 29, 2016

### haruspex

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

13. Jul 29, 2016

### andrevdh

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

14. Jul 29, 2016

### haruspex

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.

15. Jul 29, 2016

### andrevdh

Ok. Got it now.

16. Jul 29, 2016

### 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.

17. Jul 29, 2016

### 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?

18. Jul 31, 2016

### 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:
$$\rho=1,183.7=[k(16+2)+14][\frac {gr}{mol}]\cdot 13.8[Mol]~~\rightarrow ~~k=4$$

19. Jul 31, 2016

### haruspex

Yes,that's fine, but in post #8 you wrote
I guess you just got it backwards when posting.

20. Jul 31, 2016

### 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.

21. Aug 1, 2016

### haruspex

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

22. Aug 1, 2016

### Karol

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