Brownian Motion
Properties of Matter

Brownian motion and diffusion

for 14-16

These experiments together provide strong evidence for the random motions of particles in every state of matter.

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Brownian motion in a smoke cell

Brownian Motion
Properties of Matter

Brownian motion in a smoke cell

Practical Activity for 14-16

Class practical

This is a classic experiment that gives strong circumstantial evidence for the particulate nature of air.

Apparatus and Materials

  • Smoke cell, incorporating a light source and lens (Whitley Bay pattern)
  • Microscope, low power (e.g. x10 objective, x10 eyepiece) and large aperture
  • Power supply, 0 to 12 V, DC
  • Microscope cover-slip
  • Smoke source (e.g. paper drinking straw)

Health & Safety and Technical Notes

Teachers must ensure that light from the Sun is not reflected up through the microscope. (Once the cell is in position, the stage aperture is covered, removing the hazard.)

Read our standard health & safety guidance


If a camera is available for the microscope, you can demonstrate this experiment quickly to the whole class by following the camera instructions. However, seeing for yourself has much to commend itself in this case.

The smoke can come from a piece of burning cord using a dropping pipette or a burning straw (preferably paper). The straw should burn at the top and then be extinguished. The bottom end of the straw should poke into the plastic smoke container.

The cell may need to be cleaned if a waxy or plastic straw is used.

Remove the glass cell from the assembly to clean it. Afterwards, push it fully back into the assembly. It may help to wet the outside of the glass tube. You will find it helpful to clean the glass cell after every five to ten fillings to obtain the best results; otherwise the light intensity is reduced.

The cell is illuminated from one side to make the smoke particles visible under the microscope. A small piece of black card prevents stray light from the lamp reaching the eye. The lamp is placed below the level of the glass rod in order to minimise convection.

Alternative method Use a visualiser with a data projector and screen to enable students to observe Brownian motion in a suspension containing tiny polystyrene spheres.

Procedure

  1. Fill the cell with smoke using a dropping pipette and cover it with a glass cover-slip. This will reduce the rate of loss of smoke from the cell.
  2. Place the cell on the microscope stage and connect to a 12 V power supply.
  3. Start with the objective lens of the microscope near the cover-slip. While looking through the microscope, slowly adjust the focus, moving the objective lens away from the cover-slip, until you see tiny dots of light.
  4. Watch the particles carefully. Note what you see.

Teaching Notes

  • As this is such an important experiment - one of the few to show the graininess of nature and to give strong support to the idea that gas molecules are in constant motion - students should be given plenty of time to set it up and see it clearly.
  • We know what the students are supposed to see. They may not. Consequently, the students may not see what we expect. We expect them to observe jiggling points of light. The vertical component of the motion causes the bright points to go out of focus and to disappear. This will not be obvious to every student. The points of light may also have a drift velocity but we know that this observation is unimportant. The students don't know that the drift (due to large scale convection effects amongst other causes) is unimportant, and so this may become their major observation. A prepared mind helps the scientist to see.
  • Once the students know what to look for, it is useful to repeat the experiment; they'll see the expected effect second time around!
  • The bright specks of light do not bounce into each other before changing direction. Why?
  • Ask students to note down an explanation of the observations. Discuss what everyone thinks is going on and then describe (or elicit through questioning) the kinetic explanation - that smoke particles are observed as points of light, and their jiggling is due to collisions with much smaller and invisible air particles. Students should realise that an invisible movement explains an observed movement. It becomes somewhat circular when Brownian motion is (incorrectly) given as evidence of the particulate nature of air it is circumstantial at best.
  • "How big are air molecules?" "Well, smaller than the smallest specks of ash that make up smoke!" This may lead to guesstimating.
  • "1 mm across? 0.1 mm?, 0.01 mm? Or even smaller? How many smoke particles could you park side by side along the edge of a postcard (15 cm long)? This is a chance to make an order-of-magnitude guess on whether they think that there would be 100, 1000, 10000, 100000, working in powers of 10\. And now guess how many molecules you could park side by side on each smoke speck. How many is that along the edge of the postcard? Molecules must be very small indeed and atoms even smaller. Common sense tells us that."
  • Acknowledgement: This experiment comes from AS/A2 Advancing Physics. It was re-written for this website by Lawrence Herklots, King Edward VI School, Southampton.

This experiment was safety-tested in July 2007

This video shows how Brownian motion can be observed in a suspension containing micrometre diameter polystyrene spheres. Using a microscope and video camera, students can observe the motion of the polystyrene spheres. The video also shows how Brownian motion can be simulated using a vibrating loudspeaker, table tennis balls and a small balloon.

This video shows footage of the movement of particles by Brownian motion and can be used in the classroom with your students:

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Brownian motion of carbon particles in water

Brownian Motion
Properties of Matter

Brownian motion of carbon particles in water

Practical Activity for 14-16

Demonstration

Apparatus and Materials

  • Microscope with objective of relatively high power (x40 objective, x10 eyepiece)
  • Microscope slide with cover slip
  • Illuminant (lamp, lens and power supply)
  • Aquadag (colloidal graphite), photographic opaque or Indian ink
  • Flexicam and screen (optional)

Health & Safety and Technical Notes

Since this will be set up as a demonstration, there is little risk of anyone reflecting the Sun up through the microscope.

Read our standard health & safety guidance


Make a suspension of carbon in water by adding a pinhead-sized speck of colloidal graphite to a few ml of distilled water. The microscope needs a higher power objective than that used in the experiment...

Brownian motion in a smoke cell


...preferably used as a water immersion lens.

Do not leave the water in contact with the objective for any longer than necessary.

Procedure

Observe the Brownian motion of the bits of carbon in the water, by putting one (tiny) drop of solution on the microscope slide and adding the cover slip. If the particles cannot be found, try adding a drop of distilled water to the top of the cover slip and lowering the objective into it.

Teaching Notes

  • If you are teaching about gases, beware of showing this in place of Brownian motion in air.
  • Obviously, the particles observed in this experiment will be moving more slowly than fragments of ash in air.
  • An alternative: use a visualiser with a data projector and screen to enable students to observe Brownian motion in a suspension containing tiny polystyrene spheres.

This experiment was safety-tested in March 2005

This video shows how Brownian motion can be observed in a suspension containing micrometre diameter polystyrene spheres. Using a microscope and video camera, students can observe the motion of the polystyrene spheres. The video also shows how Brownian motion can be simulated using a vibrating loudspeaker, table tennis balls and a small balloon.

This video shows footage of the movement of particles by Brownian motion and can be used in the classroom with your students:

Up next

Diffusion of copper sulfate crystals in water

Diffusion
Properties of Matter

Diffusion of copper sulfate crystals in water

Practical Activity for 14-16

Demonstration

Apparatus and Materials

  • Gas jar
  • Cover glass
  • Copper sulfate crystals (harmful)

Health & Safety and Technical Notes

Warn students who might try to taste copper sulfate that it is harmful if swallowed.

Read our standard health & safety guidance


Put a layer of large copper sulfate crystals in a gas jar of water with a cover glass over the top.

Procedure

  1. Show the newly-filled gas jar.
  2. Leave undisturbed for several weeks.
  3. Get the class to check the gas jar each week.

Teaching Notes

After several weeks, the blue of the copper sulfate will diffuse into the water. Obviously, it is helpful if the jar is not moved or knocked.

This experiment was safety-tested in February 2006

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Diffusion of copper sulfate solution in water

Diffusion
Properties of Matter

Diffusion of copper sulfate solution in water

Practical Activity for 14-16

Demonstration

It is fascinating showing how liquids of different densities can be floated on top of each other before diffusion causes mixing at the interfaces.

Apparatus and Materials

  • Gas jar
  • CuSO 4 solution, concentrated (harmful)
  • Distilled water
  • Funnel and glass tube

Health & Safety and Technical Notes

Concentrated copper sulfate solution (use 100 g in 250 ml of distilled water) is harmful. Wear eye protection while handling it.

Read our standard health & safety guidance


Photos courtesy of Mike Vetterlein

You will need clear water on top of the copper sulfate solution. There are two ways of achieving this. Either put the water in first and then, carefully so as not to disturb the water, pour the denser copper sulfate solution into a funnel in a long tube so the solution goes under the water. Or, put the copper sulfate in first and, using a piece of bent glass tubing as shown, carefully add the water, keeping its outlet just below the water surface as its level rises.

Procedure

  1. Show the newly-filled gas jar.
  2. Leave undisturbed.
  3. Get the class to check the gas jar each day.

Teaching Notes

An optional variant is to put a strong sugar solution in the lower third of the jar, then add the concentrated copper sulfate solution, and finally the distilled water. Students will then see the copper sulfate diffusing against gravity as well as with it.

This experiment was safety-tested in March 2005

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Diffusion of nitrogen dioxide into air

Diffusion
Properties of Matter

Diffusion of nitrogen dioxide into air

Practical Activity for 14-16

Demonstration

Apparatus and Materials

  • Gas jars, 2
  • Cover glasses, 2
  • Nitrogen dioxide (toxic and corrosive)
  • Translucent screen and lamp

Health & Safety and Technical Notes

Although nitrogen dioxide is very toxic and corrosive, this activity can be demonstrated without using a fume cupboard. The demonstrator should wear eye protection to handle the concentrated acid.

Read our standard health & safety guidance


You will need a jar of air and a jar of nitrogen dioxide. The latter can be manufactured in the bottom of the jar beforehand (but it must be cooled to room temperature), or it may be poured in.

The illuminated translucent screen behind the jars will make the diffusion easier to see.

Procedure

  1. Invert the air-filled jar on top of the jar of nitrogen dioxide.
  2. For a litre gas jar, put about 1.5g of copper turnings in the bottom. Add 7 ml of concentrated nitric acid from a 10-ml measuring cylinder. When the gas has almost reached the top of the gas jar, put the inverted gas jar on the top.
  3. Observe the consequent diffusion.

Teaching Notes

The advantage of nitrogen dioxide is that it is visible, so students can see diffusion taking place.

This experiment was safety-tested in March 2005

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Diffusion of hydrogen into air

Diffusion
Properties of Matter

Diffusion of hydrogen into air

Practical Activity for 14-16

Demonstration

Apparatus and Materials

  • Polythene tubing, 15-cm lengths, 2
  • Blackboard chalk, soft, 1 cm
  • Soap solution
  • Hydrogen
  • Carbon dioxide (optional)
  • Retort stand, boss, and clamp

Health & Safety and Technical Notes

If gases are used from cylinders, the staff must be instructed in their proper use first.

If hydrogen is prepared chemically, safety screens and eye protecton must be used.

Read our standard health & safety guidance


Take a length of polythene tubing which is slightly too small in diameter to take a 1-cm length of soft blackboard chalk. Warm it so that it can be stretched, and push the chalk a little way into the tubing.

The hydrogen is best obtained from a cylinder, which your colleagues teaching Chemistry may be able to provide. Failing that, hydrogen must be obtained from a chemical generator, but in that case it is advisable to pass the gas through a filter of loose glass wool to remove small drops of acid which might spoil the soap film.

The top layer of chalk will get wet with soap solution in repeated experiments. Scrape it off with a screwdriver.

Procedure

  1. Hold the prepared tube in a vertical position using the stand, clamp and boss.
  2. Make a soap film at the top end by smearing soap solution across it.
  3. Feed hydrogen in through a fine tube inserted in the lower end of the polythene tubing and observe what happens.

Teaching Notes

  • The hydrogen molecules pass more rapidly upwards through the chalk than do the air molecules downwards, because the hydrogen molecules are smaller and move faster. On diffusion, the pressure above the chalk rises above atmospheric pressure and blows a bubble.
  • A control experiment is needed, to show that it is not the hydrogen from the fine tube which blows the bubble. Repeat the experiment using the second length of tubing, this time without a piece of chalk.
  • Alternative versions
  • Insert the chalk into the centre of the tubing.
  • Slip the short lengths of glass tubing into place at the two ends.
  • Then fill the two end tubes, one with hydrogen, the other with air (or, better still, carbon dioxide) and close both ends with soap film.
  • Hold the whole apparatus horizontally for a few minutes whilst diffusion takes place.
  • In this case, gravity cannot be considered to play any part.
  • Another way of showing the different rates of gaseous diffusion is to use a traditional white, unglazed, porcelain jar (such as the inner jar of a Leclanché cell).
  • The jar is fitted with a bung through which is a glass tube about 20 cm long.
  • Hold the jar upside down by a clamp stand, so the bottom of the tubing is under water in a beaker. Colouring the water helps.
  • Then place a gas jar filled with hydrogen over the top of the porcelain, and leave it there whilst diffusion takes place.
  • Hydrogen molecules diffuse into the jar faster than the air molecules diffuse out, so the pressure inside builds and the water in the glass tube is forced down.
  • The reverse effect can be shown if another bung is fitted with a length of glass tubing bent so as to point downwards when the porcelain jar's mouth is upwards. Then, with the glass tube's end under water in a beaker, lower the jar into a gas jar of carbon dioxide. This time, the water will rise up the tube.

This experiment was safety-checked in March 2005

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Diffusion of ammonia and hydrogen chloride gas

Diffusion
Properties of Matter

Diffusion of ammonia and hydrogen chloride gas

Practical Activity for 14-16

Demonstration

This is a classic demonstration that gives strong circumstantial evidence for the particulate nature of vapours. Many students may have seen this before but not have fully appreciated what it shows. As well as the diffusion of invisible particles, it also gives evidence of the difference in mean speeds of the two vapours.

Apparatus and Materials

  • Glass tube
  • Beakers, 250 ml, 2
  • Rubber bands, 2
  • Aqueous ammonia '880'
  • Hydrogen chloride (conc.)
  • Tweezers
  • Cotton wool
  • Retort stand, boss and clamp
  • Beaker of water

Health & Safety and Technical Notes

Eye protection must be worn.

It is recommended that you arrange this demonstration either in a very well-ventilated area or outdoors.

Read our standard health & safety guidance


The glass tube should be about 1 m long and 5 cm diameter.

The hydrogen chloride and aqueous ammonia should be in bottles with close-fitting stoppers.

Procedure

  1. Soak a ball of cotton wool in aqueous ammonia and insert a few centimetres into the glass tube. Rinse the tweezers in water, and dispose of excess ammonia. Close the end with the rubber bung. At the same time, insert a cotton wool ball soaked in hydrochloric acid at the other end. Rinse the tweezers again in water to avoid corrosion.
  2. Watch carefully. Where the two vapours meet a ring of thick mist will form. The position of the ring will suggest which vapour diffuses more quickly. (The demonstration takes 15 to 20 minutes.)

Teaching Notes

  • Emphasize that the particles of each vapour are moving randomly.
  • Through questioning, the students should be able to realize that the ammonia (molar mass about 17 g/mol) is diffusing more quickly than the hydrogen chloride (molar mass about 36 g/mol).
  • Further questioning can develop ideas about why the lighter gas diffuses faster. The mean kinetic energy of each gas particle is the same if the temperature is the same. Therefore, the more massive gas will be travelling more slowly and hence diffuse more slowly (why?). This is borne out by the experimental observations.

Acknowledgement: Experiment submitted by Lawrence Herklots, King Edward VI School, Southampton.

This experiment was safety-tested in June 2004

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Diffusion of bromine vapour

Diffusion
Properties of Matter

Diffusion of bromine vapour

Practical Activity for 14-16

Demonstration

A classic demonstration that is explained satisfactorily by a particulate model of gases. The students first observe relatively sluggish diffusion of bromine into air. This is followed by the much more rapid diffusion (or expansion) into a vacuum.

Apparatus and Materials

  • Vaseline
  • Brush for cleaning stopcocks, small
  • Vacuum pump
  • Pliers
  • Sodium thiosulfate solution, 500 ml 1 M (25%) or ammonia solution
  • Bromine diffusion tubes with matched accessories (see list below), 2
  • Stopcocks, 8 mm large bore, 2
  • Short length of rubber tubing
  • Borosilicate glass cap tubes to hold ampoules, 2
  • Rubber bung no. 25 with 11/12-mm hole, 2
  • Bromine ampoules, 2
  • Bucket, large
  • Retort stand
  • Translucent screen
  • Lamp for translucent screen

Health & Safety and Technical Notes

Bromine gas is very toxic and must not be inhaled. The liquid is also corrosive. The teacher must have 500 ml of 1 M sodium thiosulfate solution in a wide beaker so that a hand with a splash of bromine liquid on it can be plunged in immediately.

The main diffusion tube is a closed glass tube (45 cm long, 5 cm in diameter} with only one opening to a side tube. There is, therefore, no danger of an accident releasing bromine to the pump when diffusion into a vacuum is done. A rubber bung fits into the side tube and carries the glass tube of the stopcock. The glass tube from the stopcock extends through the rubber bung, thus ensuring that only bromine vapour and not liquid comes into contact with the bung. In any case, the bung can and should be replaced, after a few days' use.

The tube in the rubber bung leads to a stopcock with large bore. This should be of good quality, such as Interkey, with bore at least 8 mm. The tap of the stopcock must be spring-held for safety (but the stopcock may be of ordinary quality, not the special high-vacuum quality). The glass tube that leads out on the other side of the stopcock is joined to a closed glass cap by a short section of rubber tube, in which the bromine capsule is to be broken. That rubber tubing must have a fairly thin wall so that it can be squeezed with pliers to crush the capsule.

With this arrangement, the breaking of the capsule to release bromine is done separately, before the stopcock is opened to admit bromine to the main tube. This enables the experimenter to concentrate on the crushing of the capsule first and then pay full attention to the main experiment.

Note: the rubber tubing should not be very short, otherwise there is a danger of pulling it off the glass tube when squeezing it with pliers. Rubber tubing must, of course, have a bore large enough to let the capsule slide into it. The tube belonging to the stopcock and the cap tube must be still larger, so that the rubber tube fits tightly on them.)

If the apparatus meets the above criteria, the experiment may be done in the open laboratory using safety screens. If there is any doubt, the demonstration should be done in a fume cupboard.

Read our standard health & safety guidance


Rubber tubing should be 125 mm in length with an internal diameter of 12 mm to fit the stopcocks tightly.

The bromine moving into the diffusion tube is more clearly seen if a translucent screen, illuminated by a rear lamp, is set up behind it.

Cleaning the apparatus: After the experiment the whole apparatus should be put into a bucket, prepared in readiness, half full of ammonia solution. The apparatus should then be taken to pieces under the solution in the bucket. The lower end of the apparatus should be plunged in first, the bung should be removed from the main tube and the stopcock and other items disassembled. The apparatus can later be washed, dried and reassembled. Vaseline should be used to lubricate the stopcock, not tap grease.

It is sensible to wear rubber gloves for this cleaning process. Rubber gloves are not necessary during the main experiment. This would only invest the experiment with an air of danger which it does not deserve if carried out as suggested. If the apparatus has to be cleaned and dried quickly for use with another class, a hair dryer, with heater, provides much the easiest way of drying the main tube.

Procedure

Diffusion into air Initially the bromine capsule is placed in the glass tube and the tap is closed. The diffusion tube is full of air.

  1. Slide the capsule down from the glass tube into the rubber tubing.
  2. Using square pliers, not side-cutters, break the capsule by squashing the rubber tubing. This will release liquid bromine and it will run towards the tap.
  3. Watch carefully as the tap is opened so that bromine moves into the diffusion tube.
  4. Measure how far the average bromine molecule (average density of 'brownness') moves in about 20 minutes. Calculate the average speed of a bromine molecule.

Diffusion into a vacuum Initially, only the bung and tap are attached to the diffusion tube.

  1. With the tap open, use a vacuum pump to extract air from the diffusion tube.
  2. Once the air has been extracted from the tube, close the tap and remove the vacuum pump.
  3. Using rubber tubing, attach to the tap the glass tube with a bromine capsule inside.
  4. Slide the capsule down from the glass tube into the rubber tubing.
  5. Using pliers, break the capsule by squashing the rubber tubing. This will release liquid bromine and it will run towards the tap.
  6. Watch carefully as the tap is opened so that bromine moves into the diffusion tube. It happens almost instantaneously!
  7. Photo courtesy of Mike Vetterlein

Teaching Notes

  • The crucial point to these demonstrations is that the average speed of bromine molecules does not change from one demonstration to the next. Careful questioning of the class will highlight many common misunderstandings. These include the idea that the bromine is being sucked into the tube in the vacuum demonstration.
  • It may be best to discuss precisely what has been observed without any theoretical inferences. This can be followed up by developing a theoretical explanation of the observations based on the particulate picture of a gas.

This experiment comes from:

AS/A2 Advancing Physics


This experiment was safety-tested in June 2004

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Brownian motion: facts and myths

Brownian Motion
Properties of Matter

Brownian motion: facts and myths

Teaching Guidance for 14-16

Robert Brown is correctly referred to as having observed the jittering motion of small particles. But he did not observe the motion of actual pollen grains. How many text books and other resources continue to hand on this mistake?

A 2001 paper published in Nature alleged that the first recorded observation of what we now call Brownian motion was made in 1785 by Jan Ingenhousz using charcoal dust [Ref: Nature, 7 June 2001 p 641]. This appears not to be the case. See the Microscopy website...

Microscopy


The webpage may also be of interest for its two short videos showing Brownian motion, one in whole milk and the other in a smoke cell.

Having used particles derived from living matter, Brown had to try several other inanimate substances to convince himself that the motion he observed was not something to do with a life force, but a property of all microscopic matter. This systematic investigation is what won for Brown the accolade of having the jittering motion named after him, work that Ingenhousz didn't need to do.

Today's research into nano-technology now routinely fabricates nano-particles. Controlling them suspended in liquids is quite a task. One method is to use a direct current controlled by a feedback system to cancel out the Brownian motion. The position of the 20 nm polystyrene spheres is monitored by a fluorescence microscope and the voltage across the solution altered accordingly. So far nano-particles have been confined to within 1 micron. Alternatively, the path of the particle can be manipulated by suitable changes of the applied voltage. [Ref: Nature , 10 March 2005 p 156]

Even before the recent advent of nano-technology, Einstein's 1905 paper on Brownian motion is his most cited paper (more than for special relativity or his work on photons). It is used by scientists working on such varied topics as aerosol particles (pollution), the properties of milk, paints, granular media (powders) and semiconductors. [Ref Nature, 20 January 2005 p 216]

Thanks to David Walker for pointing out an error on this page, now corrected. Editor

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Estimate of molecular size: a more formal method

Kinetic Theory of Gases Model
Properties of Matter

Estimate of molecular size: a more formal method

Teaching Guidance for 14-16

Imagine molecules in a gas; dots spaced far apart. Add arrows to show the random motion, not all speeds (arrows) the same but speeds around the average. You could say:

'Here is a snapshot of air molecules in this room with the camera focused at one distance. To find how one molecule would move through this vast array of moving neighbours is too difficult a business. Instead, pretend that we freeze all the molecules except one and watch that one molecule go hurtling through the crowd.'

Redraw the picture showing each molecule as one round blob without any indication of velocity. Draw the path of the chosen molecule, as it moves to collide with another, as a cylinder swept out between the two molecules. The diameter of the cylinder is equal to the diameter of the molecule and its length is equal to the mean free path. Bend the path at the collision and another cylinder is swept out as shown this diagram:

The mean free path is many times longer than the separation between molecules and so the cylinder should pass many other molecules on the way to a collision.

Now move off to a separate preparatory discussion looking at such a collision in detail. Draw a large round molecule bouncing against another molecule.

'How far apart are the molecules, centre to centre, at the collision? One diameter.'

'I am now going to show you a trick for finding out how far a molecule goes before hitting another. This trick has been invented by scientists and is not what really happens but gives good results. When two molecules collide they must be 2 radii, or 1 diameter apart. Instead of drawing the collision like that, I could pretend that the molecule flying along to make the collision is much bigger, and any other molecule that it hits is much smaller. We get the same result as long as we have the centres of the two molecules 1 diameter apart at the collision. I am now going to push this to the limit and make the flying molecule have double the radius, equal to 1 diameter, and the molecule it hits have no radius at all.'

'Now we start this story all over again. Here is the artificial molecule flying along with radius equal to one molecular diameter. It sweeps out a cylinder of 1 molecular diameter in radius and collides with the artificial point sized molecule where it bends its path.'

'Think about the path swept out by this flying molecule which is possessively patrolling its "share" of the volume of the box. This volume is equal to d2x 10-7m.'

For justification of mean free path being 10-7m, see Guidance note...

Further discussion of mean free path


'We need to know the volume of space that belongs to one molecule of air in this room. The volume change from liquid air to air is about 1:750. If for liquid air each molecule of diameter, d, occupies a cubical box of side d, then the volume occupied is d 3on the average.'

750d3= d2x 10-7

d = 4 x 10 -10m

'We have found the diameter of a typical molecule of air. An atom is probably about half that size. This is certainly a rough estimate because our measurements were difficult and we made all kinds of risky moves carrying out our calculations. Yet this is a very good estimate for many working purposes. It is the right order of magnitude.

All we are really measuring here is an order-of-magnitude distance of approach at which inter-molecular forces grow large enough to have a noticeable effect. Air of course is a mixture of different gases, mainly nitrogen (about 78%) and oxygen (about 21%).

Careful measurements for particular molecules give different diameters according to the experiment chosen and the method of interpretation used. After all, the diameter of a molecule is not as definite a thing as the diameter of a steel ball. Both nitrogen and oxygen are diatomic molecules. Not only are diatomic molecules oblong but they behave as if squashy, so more violent collisions are likely to reveal a smaller effective diameter. Nitrogen molecules are very slightly larger than oxygen molecules; in their gaseous state both have effective diameters of about 3 x 10-10m.

Up next

Mean free path

Up next

Further discussion of mean free path

RMS Mean Free Path
Properties of Matter

Further discussion of mean free path

Teaching Guidance for 14-16

√N steps gives the average mean free path for a bromine molecule in its wandering amongst air molecules. That would be similar to the stride of an air molecule amongst air molecules. You can therefore conclude that an air molecule moves about 10 -7 m between one collision and the next at atmospheric pressure.

This estimate is one of the great classical approaches to estimating the mean free path of an air molecule, first used in the nineteenth century. There are other methods, depending on measurements of viscosity, Van der Waals constants, etc. The result differs somewhat according to the method chosen. For air at room temperature, older estimates gave the mean free path of an air molecule as (0.8 – 1.0) 10 -7 m but the modern value lies between (0.6 – 0.7) 10 -7 m. In the following discussion 10 -7 m will be assumed.

The number of collisions that an air molecule makes per second will be different from the experimental estimate for bromine molecules because oxygen and nitrogen molecules move faster. Combining an estimate of molecular speed with the mean free path estimate, in one second an air molecule travels 500 m of straightened out path (a distance which contains 500/ 10 -7 mean free paths). So the molecule makes 500 x 10 7 collisions per second.

Footnote on simplifications

This is very rough calculation. Any attempt to make a correction for bromine molecules being bigger would place a very unscientific emphasis on precision in one particular place in a method that is imprecise overall. Judging from the relative densities of liquids and relative molecular masses, bromine molecules have a diameter about 1.2 times that of air molecules.

That makes the ‘average diameter’ for a bromine molecule hitting an air molecules 1.1 times on average as great as for air molecules colliding. Because any mean free path depends on the collision target area (cross-section), a bromine molecule probably has a mean free path among air molecules about 1/(1.1) 2 or 1/1.2 or (0.83) times the mean free path of an air molecule among air molecules.

This approach makes no attempt to decide what kind of average should be used for the resultant in a random walk treatment. Does the estimate ‘half brown’ fit best with the root mean square average of the random walk of bromine molecules, or should you use the plain arithmetical average? Since progress is estimated in a vertical direction alone, should you take some component of velocity, or of a mean free path?

Unless you give up this simple experiment, in which students make a guess, and resort to colorimetry and density measurements, these questions remain unanswered. Nor would it be sensible to try to answer them here; that would miss the point of proceeding quickly in a simple story so that you do not lose your students on the way.

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