# Velocity of particle

1. Jan 6, 2006

### PhiJ

Does anybody know the average velocity of a particle in solution at rtp?

2. Jan 6, 2006

### Mattara

rtp :S

Do you mean standard/normal temperature and pressure (STP)/(NTP)?

3. Jan 7, 2006

### PhiJ

Oops, I still think of it as room temperature and pressure . Yes. I mean standard temperature and pressure.

4. Jan 7, 2006

### Mindscrape

Okay, more specifics? What solution? What particle? etc.

You'll probably want to use (I think it's Boltzmann's Theorem) $$<{v_x}^{2}>=<{v_y}^{2}>=<{v_z}^{2}>$$.

Then you know that $$nRT = \frac{1}{3} Nm <v^{2}>$$

Or you can pretty much do any derivation.

Last edited: Jan 7, 2006
5. Jan 7, 2006

### PhiJ

I thought that equation was just for Gases? The idea was ions in the body.

6. Jan 7, 2006

### Mattara

hmm...average velocity in a solution. Have no idea about forumlae.

I can however theorize a bit.

A particle in a solution (liquid) moves about totally random as a part of Brownian movement. The velocity also depends on the mass of the particle and the density of the solution, and the strength of the solutions intermolecular forces (ex. hydrogen bonds etc.).

Well the common gas laws (Boyle's, Charles' and the pressure law) works in both gases and liquids, which is called fluids with a common name.

Here we have another problem. Ions in the body. Let's take the human cell for example:

The cellmembrane will let some particles through and others not. Also the direction of flow relays on diffusion (osmosis in this context).

If I were to try and make a fair calculation on the average particle (ion) in the body i would have to include many variables and would probably have to resort to programming for it. There are alot more variables than i have mentioned here and a qualified guess would be 100+.

Correct me if i'm wrong but to do a rough calculation you can use the forumla given above

7. Jan 7, 2006

### PhiJ

Hmm... Another imposible problem. Should have thought about the cell membrane. That will slow things down a bit!
I thought the laws were derived from ideal gas equations assuming that particles had no attraction between them, no energy loss, small particle size etc.. If they have attraction between them, then the derivation, and hence the formulae will be wrong won't they? Then again, I may be remembering it wrong, as its a year since I was taught it.

8. Jan 7, 2006

### Mindscrape

If there are charges then it turns into an E&M problem.

Do you have any specific ion you're trying to figure out? It will matter where in the body too. This will probably be very hard to figure out.

9. Jan 7, 2006

### PhiJ

Don't worry, it was more a general interest.
Thanks for the help.

10. Jan 7, 2006

### Mattara

There is a difference between ideal gases and real gases. The ideal gas law is accurate only when it is far from the conditions at which it would liquify (this ensures that the particle has enough energy to overcome the attractive forces between them). That is for the ideal gas laws to work 1005 the gase would have to be above its critical temperature (the temperature which the gase would be liquified by preassure alone), and it must also be well below its critical pressure, which is the pressure at which the gas become a liquid when at its critical temperature