Useful Stuff for Year 10 chemists

Exams are almost here; these resources are just to jog your memories . I suggest you download the documents and study them. I’ve tried to include the kinds of things they ask for in exams. The first one is about commercial production of iron in a blast furnace. This is a process you need to know in some detail, particularly the three temperature zones and all the reactions. The second is called Using Limestone. Pay attention to the agricultural uses of limestone. The next document talks about quite a famous displacement reaction, highly exothermic, called the Thermit Reaction. It can be done in the lab, but only with very small quantities. There are some questions on the sheet, apparently without answers. It’s a test, guys. Work out how to display the answers – they are there. Check out the video – the guy did it in his back garden. You’ll find out why when you look up the video link.

Finally, water is the universal solvent. Remind yourselves about tests for water, the Water Cycle and acid rain production here.

Bonne chance, tout le monde. See you after the hols.

Making Ammonia – the Haber process

A BRIEF SUMMARY OF THE HABER PROCESS – various sources, thanks…

Haber Tower

 

ΔH=-92kJ/mol thus exothermic

The Haber Process combines nitrogen from the air with hydrogen derived mainly from natural gas (methane) into ammonia. The reaction is reversible and the production of ammonia is exothermic.

Here’s the flowchart

Notes on the conditions

The catalyst

The catalyst is actually slightly more complicated than pure iron. It has potassium hydroxide added to it as a promoter – a substance that increases its efficiency.

The pressure

The pressure varies from one manufacturing plant to another, but is always high. You can’t go far wrong in an exam quoting 200 atmospheres (200 x atmospheric pressure or 20MPa)

Recycling

At each pass of the gases through the reactor, only about 15% of the nitrogen and hydrogen converts to ammonia. (This figure also varies from plant to plant.) By continual recycling of the unreacted nitrogen and hydrogen, the overall conversion is about 98%.

The proportions of nitrogen and hydrogen

The mixture of nitrogen and hydrogen going into the reactor is in the ratio of 1 volume of nitrogen to 3 volumes of hydrogen.

Avogadro’s Law says that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. That means that the gases are going into the reactor in the ratio of 1 molecule of nitrogen to 3 of hydrogen.

That is the proportion demanded by the equation.

There is always a down-side to using anything other than the equation proportions. If you have an excess of one reactant there will be molecules passing through the reactor which can’t possibly react because there isn’t anything for them to react with. This wastes reactor space – particularly space on the surface of the catalyst.

TEMPERATURE

Equilibrium considerations

You need to shift the position of the equilibrium as far as possible to the right in order to produce the maximum possible amount of ammonia in the equilibrium mixture.

The forward reaction (the production of ammonia) is exothermic.

According to Le Chatelier’s Principle, this will be favoured if you lower the temperature. In this case, the system will respond by moving the position of equilibrium to counteract this – in other words by producing more heat.

In case you’ve forgotten, Le Chat’s P  is stated as follows –

“The equilibrium position will respond to oppose a change in the reaction conditions”.

What this means in practice is:

If you remove a product, the equilibrium mixture changes to make more product. It tries to get back to the composition it had before the product was removed. You can carry on removing product until all the reactants have turned into product (quite useful!).

The reverse is also true. If you remove a reactant, the equilibrium changes to make more reactant (generally not useful).

In order to get as much ammonia as possible in the equilibrium mixture, you need as low a temperature as possible. However, 400 – 450°C isn’t a low temperature!

Rate considerations

The lower the temperature you use, the slower the reaction becomes. A manufacturer is trying to produce as much ammonia as possible per day. It makes no sense to try to achieve an equilibrium mixture which contains a very high proportion of ammonia if it takes several years for the reaction to reach that equilibrium.

You need the gases to reach equilibrium within the very short time that they will be in contact with the catalyst in the reactor.

The compromise

400 – 450°C is a compromise temperature producing a reasonably high proportion of ammonia in the equilibrium mixture (even if it is only 15%), but in a very short time.

Why do we need ammonia so much? 14 uses for ammonia here

 

 

Power, Work and Energy

When work is done, energy is transferred.

Rub your hands together, hard. They get hot. There’s no way someone could tell whether you’d dipped your hands into hot water or applied a force against the frictional resistance of your palms – done mechanical work on them in other words – the result is the same. Hot hands.

Work = force x distance moved by the force along the same straight line

J = N x m (joules = newtons x metres)

If I clamber up a vertical ladder 4m high, I have moved my weight (800N) 4m against gravity. I have done 800×4 = 3200J of work to do this. Looking at it another way, I have acquired 3200J of gravitational potential energy.

Work done and energy transformed are two halves of the same coin.

One more thing. The route that I take makes no difference to the work that I do or the energy transferred. Walking up a spiral staircase to get to the top of the Eiffel Tower does exactly the same amount of work on me as if I’d used the elevator, since my weight is being transferred through the same vertical height. There are stern warnings about hurling objects – even small ones – off the summit of the Eiffel Tower. I wonder why….? You might try to work out how fast an object would be going at ground level, given that the top level is at a height of 276m. Plus or minus 15cm, depending on expansion due to temperature differences….Oh, forget about air resistance. I’ll post the answer, but do try to work it out for yourself.

Here’s a little problem:

For those who like exercise, you can walk almost up to the top.

The actual count of stairs includes 9 steps to the ticket booth at the base, 328 steps to the first level, 340 steps to the second level and 18 steps to the elevator platform on the second level. When exiting the elevator at the third level there are 15 more steps to ascend to the upper observation platform. Each step is 15cm high. If someone like me – my weight is 800N – walks at one step per second, work out how long it would take me, and also my average power (energy transformed per second). We can neglect the time in the elevator.

I’ll post a comment with the answer. Try it for yourselves.

Breaking Water

Water is amazing stuff.

Just one atom of oxygen and two of hydrogen. Splitting it into these parts turns out to be quite easy. If you’ve a couple of pieces of platinum to spare…Water undergoes a decomposition reaction under electrolysis.

The Hoffmann voltameter was the original apparatus for electrolysing water, invented by August Wilhelm von Hoffmann (1818–1892). It consists of three joined upright cylinders, usually glass. The middle cylinder is open at the top to allow addition of water and an ionic compound to improve conductivity, such as a small amount of sulphuric acid. A platinum electrode is placed inside the bottom of each of the two side cylinders, connected to the positive and negative terminals of a source of electricity. When current flows, gaseous oxygen forms at the anode and gaseous hydrogen at the cathode. Each gas displaces water and collects at the top of the two outer tubes. It can be tested in the usual way, relighting a glowing splint for oxygen and the pop test for hydrogen. Here’s a picture of one.

Can we make one in school? Yes – here’s what to do.. Look at the diagram. Fill the large gas jar with 0.1 M sulphuric acid almost to the top and hang the electrode assembly over the rim. Lower the burettes into the acid with the taps open until the open ends rest on the bottom of the jar. Close the top and lift one burette to surround one electrode. Repeat with the other burette and support them in clips as shown. Connect the voltameter into a series circuit of rheostat, ammeter and DC supply. Switch on. A current will now flow. The rheostat can be adjusted to give a suitable current of about 0.5 A. Bubbles will be seen at both electrodes and gas can be collected in the inverted burettes.

Things to notice:

We get twice as much hydrogen as oxygen. Why?

What will the equations look like?

The complete equations can be found in this document

Aluminium from Bauxite *updated*

Aluminium is quite reactive, so can’t be extracted using a blast furnace or similar.

The extraction of aluminium from its ore is expensive and not very easy, but because it’s light and alloys easily, Al is so valuable that it’s worth the effort. Australian Al is mostly mined as bauxite – a composite of various hydrated Al ores.

Bauxite looks like Martian sand – not very interesting, but here’s an image anyway.

Round here, Bahrain has bauxite mines also. Bauxite melts at more than 2300K  – impossibly high – which would waste a lot of heat if we had to melt it ‘as-is’.

Cryolite (Na₃AlF₆, sodium hexafluoroaluminate) is a rare mineral identified with the once large deposit at Ivigtût on the west coast of Greenland, which ran out in 1987. The difficulty of separating aluminium from oxygen in the oxide ores was overcome by the use of cryolite as a ‘flux’ to dissolve the oxide mineral(s), making them a liquid at much lower temperatures, thus saving money which would otherwise be used to heat the ore up to its much higher melting point. Cryolite itself melts below 900°C (1173K), which is quite achievable and it can dissolve the aluminium oxides sufficiently well to allow easy extraction of the aluminium by electrolysis. Considerable energy is still required for both heating the materials and the electrolysis, but it is much more energy-efficient than melting the oxides themselves. Today, natural cryolite is too rare to be used for this purpose, synthetic sodium aluminium fluoride is produced from the common mineral fluorite for this purpose.

The point here is we need the purified aluminium oxide from bauxite in liquid form so the ions can move to be able to electrolyse it to extract aluminium. But, its melting point is too high, hence the cryolite.

How does it work? Here’s a schematic of the apparatus.

with thanks to blogspot for image replacement

Notice the actual casing is the cathode. The carbon graphite anodes are attacked by the oxygen produced at them and need changing quite often.

Here are the equations:

Al⁺⁺⁺ + 3e^– → Al

electrons gained  at cathode by Al – REDUCTION of Al

2O^— → O₂ + 4e^–

electrons lost at anode by oxygen ions – OXIDATION

Please notice that no electrons are lost or gained overall, their movement is a flow of charge around the circuit which we could measure with an ammeter.

For information: the electrical energy needed to produce aluminium is relatively high. To make 1kg of aluminum requires about 15 kilowatt-hours of electrical energy. This amount of aluminum can be used to make about 50 Coke cans or an energy equivalent of a 100 watt light bulb burning for three hours is needed to make one aluminium can.

Metals, Reactivity and King Canute

I crossed out Li and Sn because they didn't fit in the mnemonic, or memory aid.

Some metals are very boring and unreactive meaning they don’t easily take part in chemical reactions, if at all. Gold and platinum are like this. They don’t form oxides by reacting with oxygen in the air, even if heated strongly, and they don’t react with water either.  Just as well, really – what’d be the point of a ring that fizzed away to nothing in a puff of hydrogen every time it rained?

Some metals are very reactive. They easily – even enthusiastically take part in chemical reactions to make new substances.

Magnesium from Group 2 is like this. If it is heated in a Bunsen burner, it almost immediately ignites and burns with a brilliant white flame, forming basic magnesium oxide, a white powder.  Get your sunglasses on – this is bright!

Some people talk about acids as proton or hydrogen ion donors. Not quite true – a pickpocket doesn’t ask before he steals your wallet, and you don’t give it to him – he just takes it from you. Metals above HYDROGEN in the reactivity series steal the negative ions attached to hydrogen from acids in solution, making a metal salt and hydrogen gas. I’ve put hydrogen in the right place for you, between lead and copper.

Group 1 metals, having only one electron in the outermost shell are highly reactive. Francium is the most reactive – it’s incredibly rare and desperately expensive and its electron is a very long way from the nucleus, so it loses it easily. You won’t see Fr in a reactivity series, however – at least, not this one.

Now for King Canute. This is a ‘nearly mnemonic’ to help you to remember the order of reactivity of some common metals. Almost a thousand years ago, Canute was ‘king of all England, and of Denmark, of the Norwegians, and part of the Swedes’.  Canute had learned that his flattering courtiers claimed he was “so great, he could command the tides of the sea to go back”. Now Canute was not only a religious man, but also a clever politician. He knew his limitations – even if his courtiers did not – so he had his throne carried to the seashore and sat on it as the tide came in, commanding the waves to advance no further. When they didn’t and he got his feet wet, he had made his point that, though the deeds of kings might appear ‘great’ in the minds of men, they were as nothing in the face of God’s power. Nice.

Here’s the mnemonic using symbols for the metals… H is in yellow so everything above it is a thief!

King Canute Never Managed, Although Zealous For Publicity, He Couldn’t Haggle Against Authority.

OK, calcium and sodium (the ‘a’ is missing from Na) are the wrong way round, also the ‘n’ and ‘e’ is missing from zinc and iron, but it’s nearly there – and it helps. I was taught this one forty-five years ago, and I can still remember it…Eugh!

The Fate of the Universe

 

 

 

 

 

 

 

The WMAP gives better resolution. The Universe is anisotropic. Bumpy, in other words

It’s ironic that the mathematics for the very large grew out of quantum mechanics – the maths of the very small. Imagine the universe during the first tiny fraction of the first second. Random chance, arising from quantum uncertainties, allows for some areas of space to have slightly more matter and energy than other areas of space.  This isn’t much different from the observation that the density of air has slight variations across a room.  But then if space itself grows quickly, those slight density fluctuations will be turned into big density fluctuations which act as the seeds of large scale structure.  This happens because the areas with greater density have stronger gravitational forces, and the particles in these regions attracted each other more rapidly than those in the areas of lower density.  Over many billions of years, this led to the structure we see: galactic clusters formed from the high density regions, leaving behind the empty spaces.

 

The images are CMB satellite maps of the Universe, one from COBE – COsmic Background Explorer, the other from the Wilkinson Microwave Anisotropy probe, or WMAP, detecting temperature differences of 0.0002 degrees Celsius

If we look at the evidence from redshift, also the brightness of supernovae, we observe that for a particular redshift the supernova ought to be brighter than it actually is, suggesting that it’s not just moving away with constant speed, it’s also accelerating. Gravity wants to pull the pieces together, expansion (driven by who-knows-what – a fifth fundamental force, perhaps), wants to push it apart. if there’s enough matter, gravity will win and the Universe will collapse, if not, expansion will win and the Universe will continue to expand forever.

There’s more. Individual galaxies within clusters such as the Virgo Cluster move much faster than anticipated.  Since the motion of the galaxies stems from gravitational forces, this observation indicates that there is more mass inside the cluster than can be seen.  The gravitational forces of this greater amount of matter lead to higher velocities. This is the evidence for so-called ‘dark matter’.

Whatever the fifth force – if it exists – is, that drives the expansion of empty space, is invisible.  And it has no gravitational effect; in fact it has an ANTI-gravitational effect, so it can’t be ordinary matter.  For these reasons, and for a few more subtle reasons, cosmologists have given this mysterious stuff the name ‘dark energy’.

Recent results now indicate that 70% of the energy density of the universe is dark energy. The remaining 30% is matter, but only a tiny fraction of this, about 0.1%, is visible matter. The vast majority of the matter in the universe is dark matter, and the majority of the universe is dark energy.

What will happen? A blueshift and crunch or continued redshift? Until we’ve figured out more details about dark matter and dark energy, your guess is as good as mine…

Finally, guesswork over whether the Universe will collapse or continue expanding forever seems to hinge on knowing how dense it is.  Back to Year 8 science – density is defined as mass divided by volume. One can measure the density of the universe by observing the local group of galaxies and assuming that the Universe is all the same. One can also calculate the density required such that the Universe will eventually stop expanding. This density is called the critical density, and the ratio of the observed density to the critical density is given by the Greek letter ω. If ω is less than one, the Universe will continue expanding until it is so large that the darkness and cold will come. If omega equals one the Universe will eventually stop expanding but will not collapse. In this case, the darkness and cold will still come. But, if omega is greater than one, then the Universe is doomed to collapse under it’s own gravitational mass, and will implode in a cosmic fireball of steadily decreasing size, disappearing down a singularity like a rabbit down a hole. But don’t worry, the ultimate fate of the Universe is a few billion years away.

Omega (Density Ratio)	Fate of the Universe
ω<1	Open; Eternal Expansion, Cold Death
ω=1	Flat; Cold Static Death
ω>1	Closed; Big Crunch, Hot Death

For theoretical reasons, at the moment cosmologists like to believe that ω = 1.

Unfortunately, attempts to measure it yield results ω=0.1, or thereabouts.

Oh, dear.

Long Way From Nowhere – The Big Bang

in the beginning…in the darkened closets at the centre of our thoughts lie deep and unfathomable questions. Why are we here? Where did we come from? Where are we going? We have come a long way from  mystical beginnings to the study of cosmology and the origins of the universe.

According to the standard theory, our universe sprang into existence as a “singularity” around 13.7 billion years ago. What is a “singularity” and where does it come from? To be honest, we don’t know for sure. Singularities are zones – not even places in the geographical sense – which defy our current understanding of physics. They are thought to exist at the core of “black holes”, areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squashed into mind-bogglingly infinite density so not even light, which can be bent gravitationally, can get out. These zones of infinite density are called “singularities.”

Below the event horizon, not even light can get out

Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense ‘something’ – a singularity. Where did it come from? We don’t know. Why did it appear? We don’t know. The first evidence was when in the late 1960’s Stephen Hawking and Roger Penrose reworked Einstein’s General Theory of Relativity and arrived at the conclusion that there must have been a ‘beginning’. The singularity didn’t appear in space, there was no space before it. Secondly, Hubble’s expanding Universe is a matter of fact, redshifted galaxies are moving away from us, evidenced by spectral fingerprints and the greater their distance, the greater their recession velocity, as the fabric of spacetime expands. Thirdly, if the universe was once very, very hot as the Big Bang suggests, we should be able to find some remnant of this heat. In 1965, radio astronomers Arno Penzias and Robert Wilson discovered that the temperature of the Universe isn’t absolute zero, instead a 2.725K Cosmic Microwave Background radiation (CMB) pervades the observable universe and is thought to be the heat signature everyone was looking for. Their discovery brought Penzias and Wilson the 1978 Nobel Prize for Physics. Fourthly, H and He are abundant, instead of heavier elements requiring more energy to create them.

In the first 10^-43 seconds, time was not. This is the so-called ‘quantum of time’, or the Planck time – the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length l(p).  Derived, interestingly from three fundamental constants.

The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning, roughly equal to about 10^-20 times the size of a proton.

The ‘quantum of time is the smallest measurement of meaningful time. Within the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10^-43 seconds.

This timeline summarises the rest…

Click on the image to enlarge it.

Within a ridiculously small fraction of a second, the universe expanded enough, and thereby cooled sufficiently, for the fundamental interactions (or ‘forces’) to evolve into the ones we know about today.  Very soon after that, but still only a fraction of a second old, the fundamental particles in the universe were cool enough to condense into protons and neutrons.  After about 100s, the protons and neutrons were cool enough to begin to form nuclei.  The energy density of the universe at this point was still dominated by radiation, however.  This intense and hot radiation continuously bombarded the protons, neutrons and electrons in the universe.  After about 50,000 years, the universe was cool enough that the matter overcame the radiation domination in the total energy density.  At this point, called the epoch of matter domination, gravitational effects began to become important.  After about 400,000 years, the universe was sufficiently cool and the density sufficiently low for electrons and protons to form hydrogen atoms.  This epoch is called recombination.

At that point, the radiation stopped interacting constantly with the matter in the universe.  This is called decoupling.  The temperature of the universe at that point is thought to have been about 4700⁰C.  Think of the radiation as having been emitted from every point (in space) in the universe, with an intensity proportional to the matter density at that point in space.  It is expected that this radiation should be observed today, but red-shifted by an amount due to the expansion of the universe since the time the radiation was released.  This radiation from decoupling is the CMB.

But the big bang model alone cannot explain all of the observations.  In particular, it cannot account for the inhomogeneities seen in the CMB, meaning the structure of the Universe isn’t perfectly smooth, neglecting little gravitational blips because of galaxies, or indeed the large scale structure of galaxies.  Also, the big bang does not predict the fate of the universe.  Will it expand like this for ever?  Will it collapse back on itself?

Torricelli’s Barometer

Evangelista Torricelli was born on October 15, 1608, in Faenza, Italy and died  quite young on October 22, 1647 in Florence, towards the end of the great period of enlightenment known as the Renaissance. In 1641, Torricelli who was interested in physics and maths, moved to Florence to work with and learn from the renegade astronomer Galileo. who got into dreadful trouble with the Catholic Church by daring to suggest that “the sun was the centre of the world, and immovable, and that the earth moves”

Simply put, a barometer measures the pressure of the air above us. The pressure of the air on a dish of mercury can support a column of mercury over three quarters of a metre high. Here’s how to make one. Fill a tall glass tube with mercury right to the top. Hold your finger over the end and invert the tube underneath a dish of mercury. Take your finger away and the mercury level falls a little, creating a near-vacuum with a little mercury vapour. The atmosphere pushes down on the mercury in the dish and supports the weight of mercury in the inverted tube. For a long time, atmospheric pressure, just over 100kPa, was quoted as ‘760 millimetres of mercury’. You can work the calculation yourself. Mercury has a density of 13.6 x that of water, 13,600 kg/m³. h = 0.76m and g = 10m/s². P = hdg. What do we get? Just over 100,000Pa or 103kPa.

Torricelli’s ideas that the weight of the air from the atmosphere caused the liquid to stop falling seemed to be confirmed.

Here it is...

Torricelli also noticed that the level of the fluid in the tube changed slightly each day and concluded that this was due to the changing pressure in the atmosphere. He wrote: “We live submerged at the bottom of an ocean of elementary air, which is known by incontestable experiments to have weight”. 

 

And, of course, if air has weight, it must also have pressure…..

On a practical note: teachers were allowed to make these in front of their students, then somebody realised that mercury vapour, a heavy metal, was incredibly poisonous so we weren’t allowed to do it any more. Sorry, all.

How to Revise

Exams aren’t much fun, are they. Still, here’s a few ideas to help make them feel a bit less like a visit to the dentist.

Stop worrying about what you don`t know and start focusing on what you do know. Knowing at least one thing about your subject is the start from which to develop your knowledge.

Plan ahead. Decide the areas you are going to revise and give them an order of priority. Sometimes it is a good idea to revise the most difficult bits first. Then the rest is much more fun.

Organise regular breaks and fill them with something you like doing – listening to music, making a phone call, going for a walk or surfing the net. Make sure they are shorter than your revision time.

Revise with a friend if that works for you. Write answers to predicted questions and test each other on any lists or data you have to memorise.

What do you learn with ease? Telephone numbers, words of songs, software instructions? Think about how you do it and work out if you can apply the same technique to your revision.

Talk to someone who is good at revision and find out how they do it. Are there any tips you can use?

Don’t just sweat it the night before – it doesn’t work. ‘Revise’ means ‘look again’ – the more times the better.

You can only really concentrate for twelve minutes without changing task. Remember that!

Don’t just try to memorise the book – that won’t work – you need the basic facts at your fingertips which you’ll be able to use.

Imagine yourself in the exam, turn over the paper and smile, knowing you can answer the required number of questions. Keep repeating this exercise and make it fun.

Decide a cut off time the day before and definitely take the evening off.

Delete any negative thinking like “I am going to fail, I don`t know enough” and replace it with “I can pass this exam, I have stored plenty of information in my brain.” Keep repeating any positive phrases even if you don`t believe them.

Make a list for each exam of any equipment you need. Pack your bag in advance.

Keep yourself to yourself before entering the exam room. Don`t listen or join in with others` anxious chatter. Arrive at the exam room just a few minutes before it starts.

Concentrate on breathing slowly and steadily. Attend closely to your breathing and know it will help you stay focussed in the exam.

As you read the questions remind yourself that “I have revised well and can answer all that I need to.”

Arrange to do something  fun after the exams. Think forwards rather than focusing on something you can do nothing about.

Prioritise – decide which topics are most important for today. Concentrate on those.

Practise answers to questions and then learn them. This is really, really important!

Prepare key points and devise fun ways to remember them – colours, objects, mnemonics, cartoons.

Timetable study time and leisure or free time – reward yourself with each task completed.

Find a friend to work with as long as you don`t just distract each other.

Stay cool and remember to breathe!

Make a list of all that you know already, compare with your revision list – this will show up any gaps in your learning

Reward yourself for each task completed – a cookie, a stick of gum..

If you can work with friends then make time to test each other and swap revision tips.

Use any methods that have worked for you before.

In the exam: Read all the questions as you go along. It’s a mark a minute, roughly.

In the exam: If there’s three marks allocated try to write three important things down.

In the exam: Don’t waffle. It upsets the marker who is looking to find marks for you.

In the exam: Stick to your timings – it`s better to have something for each than one stunning answer and the rest blank. Your priority may be influenced by how much you know for each subject.

In the exam: If you`re stuck for recall it`s a good idea to look up and to the left – don`t ask me why, try it, it works.

In the exam: Don`t panic. When you panic you use up all the energy you could be using in your exam. Think about how you`ve remembered and written answers successfully in the past.

Finally – exams are there to be PASSED, not to fail. Carpe diem! Seize the day!

Fluid pressure

Compares pressures

This is a manometer. It’s just a plastic U-tube half-filled with coloured water. Attach one end to the gas tap. The gas pressure pushes down on one side, pushing the other side up. We can say that the excess pressure over and above atmospheric pressure is supporting a column of water 4.9cm or 0.049m high. We can then use

P = hdg

to work out this pressure in Pascals .

Let h = 4.9cm or 0.049m. Look at the picture, people….

The density of water is 1000kg/m³ and g is about 10m/s²

so, excess pressure, P, over and above atmospheric pressure

P = 0.049 x 1000 x 10 =490Pa

Not difficult, is it?                 Thanks, Sheikha…

The weight of air above us is quite another matter, however. Let the air above us be just over 8km high and of uniform density of 1.2kg/m³. It isn’t, of course, the further up we go, the less dense the air, but the atmosphere extends to, well, space at a height of about 100km, so if it was of uniform density, it’d be about five miles or 8km high

Using P = hdg:

P = 8,000 x 1.2 x 10 = 96,000Pa – more or less 100kPa. Huge. What does this incredible pressure do to us? Well, nothing since the air in our lungs is also at this pressure, so the pressures outside and inside balance out. But, what if they didn’t? Our lungs would collapse as if an elephant had trodden on our chest! We can show what happens in the lab. Have a look at this..

Squashed!

The can is like a petrol can (but empty, of course!). Put a little bit of water in the bottom, open the lid and heat it with a bunsen burner. The water boils, steam driving all the air out of the can. Screw the top on quickly to prevent the air rushing back in. The pressure inside is small – it’s a partial vacuum in there. But, the air outside is still at 100kPa – look what happens to the can…

Electron Diffraction

Light is a wave, right? No, said Einstein, when he discovered the photoelectric effect, it’s a particle. A light-bullet, or a photon with  energy = h x frequency which is equal to hc/λ. Actually, it’s both.

But, we’ve been here before.

Electrons are particles, right? No, they’re waves, fitting around a tramline round a nucleus, the length of which is arranged so that the electron fits nicely as a standing wave around the orbital. Have a look at this little animation and try to fit a few waves around a circle.

The image is an electron diffraction photograph of a  crystalline structure like salt which indicates that the wavelengths must be very small indeed since the apertures are of the order of interatomic distances. Electrons don’t penetrate matter very well, so this is a thin film crystal – in two dimensions, more or less.

Confusing, isn’t it… Some properties are best explained using a particle model, others by a wave model.

If electrons are wavelike, they should have a wavelength and thus should be able to be diffracted.  Wavelength first. Count Louis de Broglie (pronounced ‘de Broy’) came up with this in 1929, ten years after Bohr’s model of the atom..

wavelength = h/momentum

λ=h/p = h/(mv)

h being Planck’s constant. In short, everything with mass that moves has a wavelength.

I wonder what the wavelength of a bowling ball might be? From a high school factbook, we learn that the maximum permissible mass of a bowling ball is 7.26kg. Assuming it travels at about 10m/s when hurled down the lane, its wavelength would be nine times ten to the minus thirty six metres. A bit too small to measure, then…

So, this is only important if masses are very small.

Photoelectricity – Light as a Particle

 

Einstein won the Nobel Prize for this. If we shine some light of a high  enough frequency on a metal plate, electrons get ejected from the plate. We can attract them towards an anode and thus measure an electric current. The more electrons emitted per second, the larger the current.

OK so far. But, is the light shining on the plate a wave or a particle?

The details of the photoelectric effect come out differently depending on whether light consists of particles or waves. If it’s waves, the energy contained in one of those waves should depend only on its amplitude – that is, on the intensity of the light. Other factors, like the frequency, should make no difference. So, for example, red light and ultraviolet light of the same intensity should knock out the same number of electrons, and the maximum kinetic energy of both sets of electrons should also be the same. Decrease the intensity, and you should get fewer electrons, flying out more slowly; if the light is too faint, you shouldn’t get any electrons at all, no matter what frequency you’re using.

Does this happen? Actually, no, it doesn’t. If the frequency is too low, no electrons at all are emitted. If the intensity is decreased but the frequency is high enough, we just get fewer electrons and even if the light is very faint indeed, we still get some.

We have to backtrack a bit now. In 1900, Max Planck was working on the problem of how the radiation an object emits is related to its temperature. He came up with a formula that agreed very closely with experimental data, but the formula only made sense if he assumed that the energy of a vibrating molecule was quantised – that is, it could only take on certain values. The energy would have to be proportional to the frequency of vibration, and it seemed to come in little “chunks” of the frequency multiplied by a certain constant. This constant came to be known as Planck’s constant, or h, and it has the value 6.63 x 10^-34 Js. EM radiation therefore can be thought of as ‘light-bullets’ – little chunks or photons which are frequency dependent. The energy of a photon therefore is E = hf or E = hc/λ

Planck actually didn’t realize how revolutionary his work was at the time; he thought he was just fudging the sums to come up with the “right answer,” and was convinced that someone else would come up with a better explanation for his formula. Einstein took him seriously.

If  the incoming photon energy  is more than the energy required by the metal to prise an electron loose from the electrostatic attraction of surrounding nuclei – the WORK FUNCTION ENERGY, different for different metals, the electron is hooked out and any remaining energy is taken up as kinetic energy of the emitted electron. So, it’s an all-or-nothing event. Too little and nothing happens. These energies are of the order of a few eV – useful when looking at the properties of new alloys for switching circuits on computers.

Einstein made the predictions in 1905 and eleven years later Robert A Millikan, also a Nobel laureate did the practical which agreed with it. Given that it all happened in the middle of the First World War, this was quite impressive.

Here’s a summary.