Reef Chemistry Question of the Day #134 Speed of molecules

Randy Holmes-Farley · Jun 17, 2015

Reef Chemistry Question of the Day [HASHTAG]#134[/HASHTAG]

I thought we'd try something different today and for the next few follow up questions.

This topic is not something I expect many people to know, but which is a neat fact to learn. So in picking an answer, if you explain your logic it might be interesting to other readers....

The movement of molecules through water and air is critical for a reef tank. Bringing O2 to organisms, for example, or removing CO2.

In order to have a good understanding of these processes, we need to understand how molecules move.

The simplest case is a gas (air) so we'll start there in this first question.

Molecules in air are constantly bouncing around off each other and off objects like you or a table. In between bounces they move in a perfectly straight line.

How fast do you think the molecules of O2 in the air in your home are typically moving between bounces (on average)?

A. 0.1 mile per hour
B. 1 mile per hour
C. 10 miles per hour
D 100 miles per hour
E. 1,000 miles per hour
F. 186,000 miles per second

Good luck!

.

JimWelsh · Jun 17, 2015

Well, the answer clearly isn't F, since 186,000 miles per second is approximately the speed of light in a vacuum!

Maxwell's speed distribution function describes the speeds of molecules in an idealized gas. It describes the probability of finding particles moving at a particular speed within the gas, given the temperature, density, and molar mass of the gas. Some particles will be moving faster than others, and some will be moving slower, but the average (mean) speed can be calculated.

This mean speed can be calculated from the distribution function, and is represented by the square root of (8 * R * T)/(pi * M), where T is temperature in degrees Kelvin, R is the gas constant, and M is the molar mass of the gas.

Let's assume T = 298.15K = 25C = 77F. The gas constant R is defined by the U.S. Standard Atmosphere (USSA1976) to be 8314.32 Joules per degree Kelvin per mole. Since air is a mixture of gasses with different molar masses, it is expedient to use an average molar mass for this calculation. The average molar mass for dry air (according to the USSA1976 standard) is 28.9645. That gives us an average speed of a typical molecule of dry air at 1 atmosphere at room temperature = Sqrt(8 * 8314.32 * 298.15 / (pi * 28.9645)) = 466.8 m/s = 1044 miles/hour.

Therefore, I say the answer is E: 1,000 miles per hour.

beaslbob · Jun 17, 2015

f

speed of light!!!!

getting them to all move in one direction is another matter.

beaslbob · Jun 17, 2015

e

1000 miles per hour is the speed of sound. so that could be also but represents how fast pressure disturbances propagate.

Chameleon · Jun 17, 2015

JimWelsh said:
Well, the answer clearly isn't F, since 186,000 miles per second is approximately the speed of light in a vacuum!

Maxwell's speed distribution function describes the speeds of molecules in an idealized gas. It describes the probability of finding particles moving at a particular speed within the gas, given the temperature, density, and molar mass of the gas. Some particles will be moving faster than others, and some will be moving slower, but the average (mean) speed can be calculated.

This mean speed can be calculated from the distribution function, and is represented by the square root of (8 * R * T)/(pi * M), where T is temperature in degrees Kelvin, R is the gas constant, and M is the molar mass of the gas.

Let's assume T = 298.15K = 25C = 77F. The gas constant R is defined by the U.S. Standard Atmosphere (USSA1976) to be 8314.32 Joules per degree Kelvin per mole. Since air is a mixture of gasses with different molar masses, it is expedient to use an average molar mass for this calculation. The average molar mass for dry air (according to the USSA1976 standard) is 28.9645. That gives us an average speed of a typical molecule of dry air at 1 atmosphere at room temperature = Sqrt(8 * 8314.32 * 298.15 / (pi * 28.9645)) = 466.8 m/s = 1044 miles/hour.

Therefore, I say the answer is E: 1,000 miles per hour.

I corrected your nice formula for the molar mass of O2 (MW = ~32) and got ~444m/s or ~994 miles per hour

DFW · Jun 17, 2015

C, because the fans in our house move air at about that speed, certainly much less than 100 mph, and certainly more than 1 mph.

JimWelsh · Jun 17, 2015

Chameleon said:
I corrected your nice formula for the molar mass of O2 (MW = ~32) and got ~444m/s or ~994 miles per hour

Yeah, I was wondering about that. I'm certain that using the MW of O2 would be correct for a pure O2 gas situation, but I'm not sure if the presence of all that nitrogen, etc., affects the average speed of the average O2 molecule in the air mixture or not. Good point, though.

Chameleon · Jun 17, 2015

JimWelsh said:
Yeah, I was wondering about that. I'm certain that using the MW of O2 would be correct for a pure O2 gas situation, but I'm not sure if the presence of all that nitrogen, etc., affects the average speed of the average O2 molecule in the air mixture or not. Good point, though.

It shouldn't. In order for the molecules to have similar kinetic energy, which they do, the more mass they have the slower they must move. Helium must move very fast

JimWelsh · Jun 17, 2015

beaslbob said:
e

1000 miles per hour is the speed of sound. so that could be also but represents how fast pressure disturbances propagate.

Actually, the speed of sound is closer to 770 MPH or so, depending on temperature, humidity, etc., but there is a direct relationship between the average speed of molecules in a gas and the speed of sound through that gas. See http://physics.stackexchange.com/qu...lation-between-speed-of-sound-and-r-m-s-speed. In the case of dry air, the RMS speed is 1.085 the mean speed I calculated above. Plugging that into the formula in the link I just gave, it estimates the speed of sound in dry air at 25C to be 773.8 MPH, which is very close to the correct answer of 774.3.

shornik · Jun 18, 2015

OK, I am not understanding a single word in any of this but it fun trying to learn. Well wait there are a few words I understand.... "very close"... "correct answer".... things like that, but that is about all.
I do have a quick question, if the answer is ~1000 mph and that is ~ the speed of sound, wouldn't we hear, or why don't we hear sonic booms from the molecules bouncing off everything?

Robink · Jun 18, 2015

Holy crap Batman!!!!!

beaslbob · Jun 18, 2015

JimWelsh said:
Actually, the speed of sound is closer to 770 MPH or so, depending on temperature, humidity, etc., but there is a direct relationship between the average speed of molecules in a gas and the speed of sound through that gas. See http://physics.stackexchange.com/qu...lation-between-speed-of-sound-and-r-m-s-speed. In the case of dry air, the RMS speed is 1.085 the mean speed I calculated above. Plugging that into the formula in the link I just gave, it estimates the speed of sound in dry air at 25C to be 773.8 MPH, which is very close to the correct answer of 774.3.

Oh yea. My bad.

I was probably thinking feet per second.

beaslbob · Jun 18, 2015

beaslbob said:
e

1000 miles per hour is the speed of sound. so that could be also but represents how fast pressure disturbances propagate.

woopsies. speed of sound is 770 or so. as pointed out below. sorry

Randy Holmes-Farley · Jun 18, 2015

shornik said:
OK, I am not understanding a single word in any of this but it fun trying to learn. Well wait there are a few words I understand.... "very close"... "correct answer".... things like that, but that is about all.
I do have a quick question, if the answer is ~1000 mph and that is ~ the speed of sound, wouldn't we hear, or why don't we hear sonic booms from the molecules bouncing off everything?

As a object moves at or above the speed of sound, the pressure (sound) waves it creates in the air (like a wake on a boat) cannot move away from the front of the object. The pressure waves (molecules) pile up on each other, creating a bigger pressure wave (hence a louder noise).

An individual molecule moving in empty space (like the space between other molecules) creates no pressure wave (no noise) since there can be no pressure in empty space. Pressure and noise are only attributes of large numbers of molecules together that can move together and apart as a pressure wave passes (like the rise and fall of an ocean wave, except in this case it is density or pressure, not height)..

A sound wave cannot move faster than the individual molecules in the air, since its movement is caused by one molecule moving forward, hitting another molecule, and that one then moving forward. Sound actually moves a bit more slowly than the molecules since not all molecules are moving exactly in line with the direction of the souind. Some are moving at an angle to it. Hence the pressure wave of sound or a sonic boon even, must move somewhat more slowly than the molecules are moving.

Randy Holmes-Farley · Jun 27, 2015

And the answer is...E. 1,000 miles per hour

Others have done the calculation so I won't bother, but to most people this seems amazingly fast!

Happy Reefing

chefjpaul · Jul 16, 2015

Thanks Randy,

but have you been asked yet....

Why the The structure of orthophosphate?

Randy Holmes-Farley · Jul 19, 2015

chefjpaul said:
Thanks Randy,

but have you been asked yet....

Why the The structure of orthophosphate?

Two reasons.

First is that it is a big factor for reefers.

Second, it has been a big part of my professional life. Two of my more successful inventions are the prescription pharmaceuticals Renagel and Renvela (sevelamer carbonate and sevelamer hydrochloride). They are phosphate binders for people with chronic kidney disease and/or are on dialysis. They prevent the absorption of excessive phosphate into their bodies from foods. There's a ton of phosphate in food, and normal people pee it out. But folks with poor or no kidney function cannot get rid of it adequately and calcium phosphate precipitates in arteries and elsewhere in the body, potentially leading to premature death from a variety of conditions. It is a polymer that binds the phosphate before it can be absorbed by the patient. Together they recently sold a billion dollars worth of drug in a year.