Atmospheric Pressure
Properties of Matter

Pressure and density of air

for 14-16

These experiments produce values for the pressure exerted by the Earth’s atmosphere at its surface and for the density of air. They can also lead to values for the mean speed of air molecules.

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The barometer

Atmospheric Pressure
Properties of Matter

The barometer

Practical Activity for 14-16

Demonstration

This introduces the barometer tube and the pressure exerted by the Earth’s atmosphere.

Apparatus and Materials

  • Barometer tube
  • Trough
  • Metre rule
  • Mercury tray i.e. large non-metallic, smooth-surfaced tray (ideally with a small drain hole in one corner fitted with a rubber bung), 2
  • Translucent screen and lamp
  • Retort stand, boss, and clamp
  • Mercury
  • Small plastic funnel

Health & Safety and Technical Notes

Read our standard health & safety guidance


Mercury vapour is very toxic but the liquid evaporates very slowly. Provided any spilt mercury is collected thoroughly, this demonstration can be done in a lab with normal ventilation. It is helpful to have two mercury trays: one on the floor for filling the tube over, and one on the bench for the barometer itself. See CLEAPSS Lab Handbook section 12.13.2 for tips.

When filling a closed tube as described below, it helps to first fill the tube until it is nearly full, up to a few centimetres of the open end. Close this open end with a finger and tilt the tube to run the air bubble very slowly to the other end of the tube and back. It will collect up any small, sticking bubbles on the way. Then fill the tube to the top.

The whole experiment could be done in front of the translucent screen and lamp. This will make it clearly visible to the class by silhouetting against the bright background.

An alternative to this method is to have an open-ended tube. One end is dipped into a dish of mercury, the other is connected to a vacuum pump, and the air evacuated. Note that if you do this, you will need a trap consisting of a strong round-bottomed flask inserted between the pump and the vertical tube. This prevents mercury entering the pump in the event of an accident.

Procedure

  1. Fill the barometer with mercury, holding it over the tray throughout.
  2. Hold a finger on the open top of the full tube and invert it into a trough of mercury. Do not remove your finger until the end of the tube is below the surface.
  3. Hold the barometer in a clamp to measure the height of the mercury column.
  4. Daily pressure measurements can be made with the barometer stored safely in a fume cupboard.

Teaching Notes

  • Students need to understand that the air pressure on the mercury in the bowl balances that exerted by the column of mercury in the tube.
  • Some students will just need to grasp that the bigger the air pressure, the higher the column of mercury. Others will cope with the argument that the pressure exerted by the column = weight of column/area on which it sits.
    • The weight of the column
    • = mass of column x g
    • = density x volume x g
    • = density x height of column x area x g
    • So air pressure = density x height of column x area x g /area = density x height of column x g
  • This could lead to some thought-provoking questions:
  • We live at the bottom of an ocean of air and air molecules create the air pressure by bouncing onto the surface of the Earth. The air pressure on the mercury outside in the bowl pushes the mercury up inside the barometer tube and the column of mercury just balances the air pressure. Now, imagine that we live in an atmosphere of mercury instead of air. How high would the mercury have to be from the floor to the top of the atmosphere if that was all there was to make the pressure that we actually live in down at the floor? Yes the height would have to be the barometer height, about 75 cm of mercury.

    Now think about the real atmosphere. How high would that have to be if it went on up and up just as thick as the air is in this room and then stopped at the top of the atmosphere and there was nothing more above? How high would that atmosphere of air have to be to make the pressure we measure here?

    An atmosphere of mercury would have to be 75 cm high, the same height as the mercury barometer height; because that is the height of mercury which can press on the base of anything with the same pressure as the whole atmosphere. How high would a water barometer have to be? We would need to know the density of water compared with mercury. So now we must go and find that comparison.

    Finally, how high would the atmosphere have to be to balance a mercury barometer or a water barometer? We would need the density of air compared to that of water or mercury.

  • Students capable of using equations of motion could work out how fast an air molecule would be moving as it reached the surface of the Earth, after falling from the top of this ocean/atmosphere and passing through the gaps between the other molecules. The result obtained will be about 20% below the actual average speed of air molecules (500 m/s).
    • This can lead to a useful discussion of estimates and the assumptions on which they are based. Also, to give it some respectability, this method was used by Boltzmann to arrive at the Maxwell distribution, with a modification for the uniform density assumption.
    • For example: If the height of a uniform atmosphere of air is approximately 8 km,
    • Then using the kinetic equation v 2 = u 2 + 2 as
    • The velocity at the Earth's surface is √(2 x 10 x 8 x 10 3 )= 400 m/s
  • Students who know pV = 1/3 nmv 2 or p = 1/3 ρ v 2 will be able to calculate the velocity of air molecules at the Earth's surface.
  • This is an astounding result; faster than a small rifle bullet and over 1000 miles an hour. Of course some air molecules are travelling faster than that and others more slowly. 500 m/s is just the average speed.
    The reason why gas molecules have a great variety of speeds is that they are frequently colliding with each other and exchanging kinetic energy in collisions so that a molecule sometimes travels faster and sometimes slower. Of course the whole lot keep the same total kinetic energy all the time. The speeds have a statistical distribution around a constant average which is characteristic of the temperature as shown in the diagrams.

This experiment was safety-tested in July 2006

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A quick comparison of densities

Atmospheric Pressure
Properties of Matter

A quick comparison of densities

Practical Activity for 14-16

Demonstration

This shows dramatic differences in the density of air, water and mercury.

Apparatus and Materials

  • Similar bottles, 3 (about 150 to 200 ml volume)
  • Domestic spring balance or a top pan balance (5 kg +/- 2 g)
  • Mercury
  • Tray to hold the bottle filled with mercury

Health & Safety and Technical Notes

Take the usual care when using mercury, but, as it is in a sealed container, it presents minimal risk.

Read our standard health & safety guidance


The bottles should be filled with air, water and mercury. All should be sealed securely and similarly. (Those sold as medical flats are suitable.)

Procedure

  1. Find and record the masses of the three bottles.
  2. Get the students to work out how much heavier the mercury is than the water, as a ratio.

Teaching Notes

  • Before the weighings, discuss the purpose of the bottle filled with air. It leads to the assumption that the mass of air is negligible compared with the mass of the container. Hence the mass of water and mercury can be calculated.
  • If possible, allow students to lift the bottle of mercury. (Insist that the bottle stays with its tray.) Their surprise at how heavy it feels will be memorable.
  • The volumes of mercury and water are the same, so the ratio of their masses gives the ratio of their densities. The absolute density can be found if their volumes are measured.
  • You could say: "Returning to the calculation of the velocity of air molecules at the base of the atmosphere, we now know that the density of mercury is about 13.5 times as dense as water. So, a water atmosphere would have to be 13.5 times as high as the mercury height, 13.5 x 75 cm: about 10 m. What about an atmosphere of air? Not air that gets thinner and thinner all the way up, but air that stays just as dense as it is here in this room?"
  • Now we are going to need a comparison of the density of water and the density of air. See the experiment:

    Measuring the density of air 3


This experiment was safety-tested in July 2006

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Measuring the density of water 1

Density
Properties of Matter

Measuring the density of water 1

Practical Activity for 14-16

Demonstration

This could be a useful introduction to the idea of density of a liquid.

Apparatus and Materials

  • Perspex box with internal dimensions 10 cm x 10 cm x 11 cm
  • Domestic balance (2 kg to +/- 2 g is adequate)
  • Cube, 1 m x 1 m x 1 m (e.g. five squares of Corriflute, 1 m x 1 m, with L-shaped wire links for the vertical edges. The fifth square sits on the top - no base is needed.)

Health & Safety and Technical Notes

Read our standard health & safety guidance


The Perspex box should have a horizontal line marked on one face, 10 cm from the internal base so it can be filled to that depth.

The metre cube could be made out of cardboard, and could be collapsible for ease of storage.

Procedure

  1. Find the masses of the empty Perspex box and then the box filled to a depth of 10 cm.
  2. Place the cardboard cube beside the Perspex box.

Teaching Notes

  • Using cubes will help younger or weaker students make the link with densities found for blocks of solids. They may need reminding that 1000 cubic centimetres = 1 litre.
  • Having found the mass of 1000 cubic centimetres of water, the metre cube can be used to help students see that the mass of a cubic metre of water would be 1000 times greater. Some may be familiar with the thought that the density of water is 1 g/cm 3 . This will help them see it cannot be 1 kilogram per cubic metre but rather 1000 kg /m 3 !
  • You could remind students that building materials like sand and gravel are sold in cubic metres and so have to be transported in strong sacks.

This experiment was safety-tested in July 2006

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Measuring the density of water 2

Density
Properties of Matter

Measuring the density of water 2

Practical Activity for 14-16

If the pan size is such that the 1 kg mass might fall off, place an open cardboard box below the pan to catch it.

Demonstration

This method uses an equal-arm balance rather than a domestic spring balance.

Apparatus and Materials

  • Equal-arm balance
  • Perspex boxes with internal dimensions 10 cm x 10 cm x 11 cm, 2
  • Mass, 1 kg

Health & Safety and Technical Notes

Read our standard health & safety guidance


The boxes should have horizontal marks, on one face, 10 cm above their internal bases.

Procedure

  1. Place a box on each scale pan to show that they balance.
  2. Add the kilogram mass to one pan and carefully pour water into the box on the other pan until the beam balances. The water will then be seen to have a depth of 10 cm, and so a volume of 1000 cubic centimetres and a mass of 1 kg .

Teaching Notes

  • An alternative is to measure out a kilogram of water and show it has a volume of 1000 cubic centimetres (1 litre).
  • A metre cube could be used to help students see that the mass of a cubic metre of water would be 1000 times greater.

This experiment was safety-tested in July 2006

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Evacuating a bottle

Atmospheric Pressure
Properties of Matter

Evacuating a bottle

Practical Activity for 14-16

Demonstration

An approach to the question: Does air have mass?

Apparatus and Materials

  • Ordinary bottle of clear glass with a well-fitting rubber stopper and glass tube
  • Motor-driven vacuum pump
  • Length of pressure tubing, 1 m
  • Hoffman clip
  • Large transparent trough (glass or plastic)

Health & Safety and Technical Notes

Use a bottle strong enough to withstand the pressure difference. Check it has no nicks or scratches.

Wear safety spectacles and use a safety screen to protect observers.

Read our standard health & safety guidance


Reject any old or perished rubber bungs or tubes for this demonstration, as they develop cracks and will not hold the vacuum.

It is advisable to use coloured water in step 3.

Procedure

  1. Connect the rubber tubing to the vacuum pump with the clip open. The bung and glass tube must be tight fitting.
  2. Remove the air by pumping and then close the clip on the rubber tubing.
  3. To show that the air has been removed, immerse the neck of the bottle (including the rubber tubing) under water and remove the clip. Water will rush in to fill the space. If the vacuum is a good one, there should be very little air inside the bottle. If the pump was not very effective or if there was a leak, then the water will not completely fill the bottle and some air will be seen in it. There will always be a small bubble left, however well the bottle is evacuated, due to air that was dissolved in the water.
  4. Repeat the experiment without pumping air out of the bottle before immersing it, in order to show what happens in that case. This should be done second to avoid using the pump with a wet bottle.

Teaching Notes

  • At this point the emphasis is on whether air has mass. How could the method of measuring the mass of a liquid be adapted to measure the mass of air? (By measuring the mass of the beaker plus liquid and then the mass of the beaker and subtracting to find the mass of the liquid.)
  • How do you know that the pump has done its job? (By putting something else, which we can see, into the empty space.) If the pump is a good one, if there are no leaks and the pump has been pumping for long enough (the pumping noise changes) then the water will fill the bottle when it is opened under water. A very small bubble of air will appear at the top, which was the air left in the bottle at evacuation or dissolved in the water.
  • It is essential to show what happens if a bottle full of air is opened under water - the water will not enter the bottle.
  • Be patient discussing the idea of a vacuum. It does not occur naturally to students, and when they have been given the idea they still do not picture it easily. It is an artificial intellectual concept. Remember that they take the air itself for granted as invisible and almost absent, as did our ancestors, including the great Greek philosophers. It was only at a late stage in the development of physical science that scientists realized that we live at the bottom of an ocean of air, which has density and exerts pressure.
  • If students ask what the pump does, the following discussion may help:
  • "The pump acts rather like a lift that is getting people out of the top floor of a tall building. A lift doesn't pull people out. It just offers them the chance to get in the lift, and the lift carries them out."
  • "The lift goes up to the top floor, the lift opens its doors and waits until a few people have wandered in. Then the door slams shut and down the lift goes. Out go the people; walking out if they are human beings, but pushed out by a moving piston in the case of air molecules in the pump. Up goes the lift again; open the doors; more people wander into the lift; out go the people. Up goes the lift... and so on. Think of that happening with a pump taking out air molecules, batch after batch, trip after trip. At that rate you will never get all the molecules out, but a pump does a very good job."

The experiment was safety-checked in July 2007

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Measuring the density of air 1

Atmospheric Pressure
Properties of Matter

Measuring the density of air 1

Practical Activity for 14-16

Class practical

This is a very quick experiment that provides evidence that air has mass. This still surprises some students!

Apparatus and Materials

For each student group

  • Party balloon, large
  • Bucket
  • Measuring jug
  • Electronic balance

Health & Safety and Technical Notes

Read our standard health & safety guidance


The bucket should be large enough to fully immerse an inflated balloon. A kitchen bin works well.

The electronic balance should be sensitive to 0.1 g or less.

Procedure

  1. Inflate the balloon.
  2. Immerse the balloon in the bucket of water and note the level the water rises to.
  3. Take the balloon out and leave it to dry.
  4. Pour water from a measuring jug into the bucket until the water level matches the level with the immersed balloon. Record how much water you added. This is the volume of the balloon.
  5. Check that the balloon is completely dry.
  6. Measure the mass of the balloon on the electronic scales.
  7. Burst the balloon near the neck. Measure the mass of the empty balloon.

Analysis

  1. Calculate mass of air in the inflated balloon in kg
  2. Calculate the volume of the inflated balloon in m3
  3. Calculate the density of air in kg m-3
  4. Compare your answer with others in the class

Teaching Notes

  • This simple experiment ignores the buoyancy of air displaced by the balloon and so is not accurate but it does yield surprisingly consistent results. Individual results can be compared and a measure of uncertainty agreed.
  • If air is particulate, it would be expected to possess mass. That it does so is shown in this experiment. However, it would also have mass if it is an infinitely extendable fluid!

This experiment was safety-tested in September 2004

Thanks to Doug Fraser for pointing out an error on this page, now corrected. Editor

Up next

Measuring the density of air 2

Density
Properties of Matter

Measuring the density of air 2

Practical Activity for 14-16

Demonstration

This rough method can produce a difference of mass of at least 8 g. With enough apparatus it could be done as a class experiment, in small groups.

Apparatus and Materials

  • Large plastic container with tap
  • Foot pump with gauge
  • Perspex box with internal dimensions 10 cm x 10 cm x 11 cm
  • Balance with a sensitivity of at least 1 g, possibly a lever-arm balance
  • Trough, filled with water

Health & Safety and Technical Notes

Read our standard health & safety guidance


You need to devise a means of coupling the pump to the container.

This might be a short length of glass tube, to fit the pump outlet, fitted with a rubber tube, to fit the tap of the container.

When the excess air is being released to measure its volume, you will need a piece of rubber tubing long enough to reach under the Perspex box in the water trough.

Procedure

  1. With the tap open, use the balance to measure the mass of the container (plus air at atmospheric pressure).
  2. Pump air into the container before closing the tap and re-weighing. The more air that can be pumped inside the better. As a rule of thumb, do not exceed 1.5 atmospheres (1.5 bars or 22 psi).
  3. Immerse the Perspex box in the water, invert and lift it so that 1000 cm3 of water is above the level of the water outside. Place the end of the rubber tubing under the box and carefully open the tap a little.
  4. When bubbles of air have replaced 1 litre of water in the box, close the tap. Refill the box with water and repeat the procedure until all the excess air has been released from the container. The last fractional filling will need to be estimated.
  5. Find the density of air from the mass of air expelled and the volume of air collected.

Teaching Notes

  • It is essential that the volume of the container should not change significantly between the two weighings. Any increase in volume will increase the buoyancy (due to the external air), reducing the measured weight.
  • You should know from the mass of the excess air how many litres there should be. Do not overdo squeezing the container!
  • Getting students to help can enhance their feeling of expectation as the last of the air is released from the container.

This experiment was safety-tested in August 2007

Up next

Measuring the density of air 3

Density
Properties of Matter

Measuring the density of air 3

Practical Activity for 14-16

Demonstration

This simple experiment gives a reasonable value for the density of air.

Apparatus and Materials

  • 1-litre flask, strong, round bottom
  • Vacuum pump, electronically operated rotary type
  • Top-pan chemical balance with a sensitivity of no less than 0.01 g
  • Measuring cylinder (1 litre capacity would be useful)
  • Bung, plastic tube and short length of rubber vacuum hose
  • Hoffman clip
  • Water trough
  • Safety screens
  • Cork ring (see technical notes)

Health & Safety and Technical Notes

Remember that vacuum pumps of this type are heavy. Two persons will probably be needed to move one from trolley to bench.

Safety screens should surround the flask before it is evacuated.

Read our standard health & safety guidance


The bung should fit the mouth of the flask snugly so that it is secure but unlikely to be forced into the flask when that is evacuated.

The glass tube through the bung should be just long enough to allow the rubber tubing to be securely fitted. The rubber tube connecting the glass tube to the pump should be just long enough to give space for the clip to be used, before detaching the tube from the pump.

A cork ring to support the flask in an upright position will help with the weighings.

Avoid using a flask with a smaller volume. The mass of the air is correspondingly more awkward to measure, and finding the density is more difficult.

Procedure

  1. Open the clip (making sure the rubber tube also opens). Weigh the flask, bung, clip, and tubes.
  2. Connect the flask to the vacuum pump to remove as much air as possible from the flask. Tighten the clip and close any inlet valve on the pump. Stop the pump and detach the tubing from the pump inlet.
  3. Weigh the flask again to find the mass of the air removed.
  4. Invert the flask over water in the trough, so that the rubber tube remains under the water surface. Carefully open the clip to allow water to fill the flask (and tubes). Then empty the water into a measuring cylinder to find its volume.

Teaching Notes

  • Seeing the water refill the flask is impressive. It also helps those who wonder whether the volume is indeed 1 litre. Even to those for whom it is self-evident that the flask has a volume of about 1 litre.
  • Getting students to realize that the mass of a litre of air is about 1 g, so that the mass of a cubic metre is about 1 kg , is no mean achievement. (Should they find the mass of the litre of air is nearer 1.2 g rams that is a pleasant bonus.) Generally, they will be surprised that air is 'so heavy!'
  • A useful extension is to estimate the volume of the room and hence the mass of the air it contains. This might lead to seeing why, living as we do at the bottom of an ocean of air, the pressure exerted by the atmosphere is so great. Comparing the density of air with that of water can lead to a discussion of the hazards of descending into the depths of the sea.
  • You could say: "Returning to the calculation of the speed of air molecules, we can move forward another step. Air has a density of about 1.2 g /litre, and water has a density of about 1 kg /litre. Air is therefore about 830 times less dense than water. The height of a column of water in a water barometer is about 10 m. If we had a uniform atmosphere of air, then it would have to have a height of 10 x 830 m; the height of the atmosphere would be 830 m or 8.3 km."
  • "However, the atmosphere is not of uniform density as can be demonstrated in the 3-D kinetic theory model, which you may remember seeing, or we could look at it again. The story we are telling is an artificial, simplified one in order to arrive at an interesting guess. Desperate measures for desperate needs."

This experiment was safety-tested in August 2007

Up next

Filling balloons

Atmospheric Pressure
Properties of Matter

Filling balloons

Practical Activity for 14-16

Demonstration

Apparatus and Materials

  • Balloons, 3, small and preferably of different colours
  • Aspirator, 10 litre
  • Rubber bungs, 3, (diameters of ends to take balloon necks stretched over them)
  • Rubber bungs fitted with glass tubes, 2, to fit aspirator
  • CO2 cylinder
  • Rubber tubing for connection to water tap

Health & Safety and Technical Notes

If gas cylinders are used, care must be taken with handling to comply with the Manual Handling Regulations. See CLEAPSS Lab. Handbook section 9.9.

Staff also need instruction in the use of regulators and (for hydrogen} the needle valve. If gases are generated chemically, see the relevant Hazcards.

Read our standard health & safety guidance


Fill the balloons immediately before display. Hydrogen, in particular, will diffuse quite quickly through the rubber of the balloon. It is helpful to work the balloon before inflating it. This is done by blowing some air into it and then stretching the rubber between the fingers so that all parts of the balloon are equally stretched. This softens the rubber and ensures the balloon blows up more easily.

Procedure

Air

  1. Connect the balloon to the top of the aspirator.
  2. Fill the aspirator with water by connecting the lower end to a water tap. The water displaces the air which fills the balloon.
  3. When the balloon is full, remove it without letting the air out and insert a rubber bung into its neck – or tie it.

Carbon dioxide and natural gas or hydrogen

  1. The procedure for filling the balloons is the same as for air, but first the aspirator must be filled with carbon dioxide, or with the natural gas or hydrogen.
  2. This time the aspirator is filled with water before its top is connected to the gas supply, that is carbon dioxide from the CO2 cylinder, natural gas from a laboratory gas tap, or hydrogen (from apparatus borrowed from the Chemistry Department).
  3. The water is drained out whilst letting in the gas at the top.
  4. Then quickly fit the balloon to the top of the aspirator in place of the gas supply. Connect the side tube to a water supply and gently force the gas out into the balloon.
  5. Hydrogen is lighter than natural gas so should be used if available.

Teaching Notes

The following balloon masses are typical:

  • Flat balloon and bung 14.5 g
  • Balloon full of air and bung 14.8 g (see note below)
  • Balloon full of CO2 and bung 19.3 g
  • Balloon full of natural gas and bung 10.5 g
  • Balloon full of hydrogen and bung 5.0 g

The balloon full of air weighs slightly more than the empty balloon even though Archimedes' Principle would appear to predict no extra weight. This is because the balloon compresses the air inside it to a slightly greater density than the air outside. (It might be as well to neglect this small difference rather than dwell on it in discussion.)

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