# A Level Physics day for teachers

Making molecules real

Prof Neil A. Downie

Air Products Plc / University of Surrey/ Royal Academy of Engineering

http://www.saturdayscience.org/

At the start of his lecture Professor Downie demonstrated some of the experiments from his book. You can see him demonstrate some of these experiments such as the carrot cannon on youtube.

http://www.amazon.co.uk/Ultimate-Book-Saturday-Science-ebook/dp/B007BOB8EU/ref=sr_1_1?s=books&ie=UTF8&qid=1375052670&sr=1-1

The carrot cannon demonstrates Boyle’s Law. You flare out the ends of a 15mm copper very slightly, by rolling a screwdriver around it (details are in the book ‘Ultimate Book of Saturday Science’). You then push the tube sideways into a large carrot, to get a carrot plug at BOTH ends. Then push a cane to push one plug, and the other plug, the bullet, comes out much faster than the cane, driven by compressed air in front of the ‘piston’ carrot.

The Law is P = K/V, where K is a constant. As you decrease the volume V between the carrot pieces at each end of the tube by pushing on the cane, the pressure P goes higher, until the static friction force F = μFn (μ = coefficient of friction and Fn is the normal force) holding the ‘bullet’ carrot is less than the force F = PA (P = pressure and A = area) from the pressure acting on the area at the back of the carrot bullet. Then the bullet shoots out.

http://en.wikipedia.org/wiki/Friction

https://en.wikipedia.org/wiki/Boyle’s_law

https://en.wikipedia.org/wiki/Robert_Boyle

The picture below left is of Robert Boyle, FRS, (25 January 1627 – 31 December 1691). He was a 17th-century natural philosopher, chemist, physicist, and inventor, also noted for his writings in theology.

The picture above right is the conventional apparatus for proving Boyle’s law (pressure is inversely proportional to volume) in a school laboratory.

http://www.nuffieldfoundation.org/practical-physics/boyles-law

The main focus of the professor’s talk was whether it was possible to actually accurately measure the molecular weight of a gas.

Relative Molecular Mass

RMM is what used to be called ‘molecular weight’. Basically, it’s the number of protons and neutrons in the atoms of a molecule. The chemists’ “mole” contains an Avogadro’s number of molecules. Avogadro’s number = 6.023 x E23

Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto, Count of Quaregna and Cerreto (9 August 1776, Turin, Piedmont – 9 July 1856) was an Italian scientist. He is most noted for his contributions to molecular theory, including what is known as Avogadro’s law. In tribute to him, the number of elementary entities (atoms, molecules, ions or other particles) in 1 mole of a substance, 6.02214179(30) × E23, is known as the Avogadro constant.

In chemistry and physics, the Avogadro constant (symbols: L, NA) is defined as the number of constituent particles (usually atoms or molecules) in one mole of a given substance. It has dimensions of reciprocal mol and its value is equal to 6.02214129(27) × E23 mol−1. Changes in the SI units are proposed that will change the constant to exactly 6.02214 x E23, when it is expressed in the unit mol−1.

Amedeo Avogadro hypothesized in 1811 that two identical volumes of an ideal gas at the same temperature and pressure contain the same number of molecules. His hypothesis is true in many circumstances and we now call this hypothesis Avogadro’s Law. It means that the molecular or atomic mass is proportional to its density at standard temperature and pressure. So if you can measure gas density, you can measure molecular mass.

The pioneers of chemistry made much of vapour density measurement in their early work. Argon was discovered by density differences, and its discovery led on to three more elements, to the separation of Ne, Kr and Xe from liquid air by William Ramsay. So density measurement has always had its place in R&D.

Ideal gas law and how you can use it to find the density of a gas: Boyle’s + Charles’ Laws Combined

https://en.wikipedia.org/wiki/Jacques_Charles

Jacques Alexandre César Charles (November 12, 1746 – April 7, 1823) was a French inventor, scientist, mathematician, and balloonist.

Charles’ law states that the volume of a gas is directly proportional to its temperature in kelvin. There are a few different methods of proving the law in a school laboratory.

https://en.wikipedia.org/wiki/Charles’s_law

The above picture shows the apparatus for one method for proving Charles’ law. I don’t like using this as it involves mercury.

Charles’ law and Boyle’s law together give you the ideal gas equation. This equation allows you to calculate the molecular weight of the gas if you know its density.

http://en.wikipedia.org/wiki/Ideal_gas_law

P V = n R T

P is absolute pressure in Pa

V is the volume of the gas in m3

n is number of moles

R is the molar gas constant 8.31 J/K

T is absolute temp in K

Mass = n . RMM

Density ρ = mass/volume = n . RMM / V

Following a bit of algebraic jiggery pokery, we have

RMM = ρ R T / P

Relative molecular mass of a molecule is also defined as the average mass of one molecule of a substance when compared with 1/12 of the mass of an atom of carbon -12.

The relative molecular masses quoted below are given at standard temperature and pressure

http://en.wikipedia.org/wiki/Standard_temperature_and_pressure

Standard conditions for temperature and pressure are standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST), although these are not universally accepted standards.

In chemistry, IUPAC established standard temperature and pressure (informally abbreviated as STP) as a temperature of 273.15 K (0 °C) and an absolute pressure of 100 kPa. An unofficial, but commonly used standard is standard ambient temperature and pressure (SATP) as a temperature of 298.15 K (25 °C) and an absolute pressure of 100 kPa.

Some relative molecular masses

Relative Molecular Masses – the heavies

Professor Downie and his colleagues have developed a piece of equipment that can measure the molecular weight of a gas. Full details will be published in a future edition of school science review. It is based on the fact that a vibrating object will have different vibrating frequencies if it is placed in different gases.

The basis physics behind the device is something that all A level physics students learn about and this is simple harmonic motion.

When you suspend a mass m (technically m should be the mass of the object and the spring) from a spring of spring constant k, you create a harmonic oscillator (see below):

The equation of motion of the harmonic oscillator system is given by:

F = ma = md^2x/dt^2 = -k x where F is the restoring force on the spring, a is the acceleration of the oscillating system and x is the displacement of mass m from the equilibrium position.

The solution is:

x = xo sin (2πft) xo is the maximum amplitude of the oscillation

where the oscillation frequency f is given by :

f = 2π √{ k/m }

It is this frequency that is modified in gas of density ρ, so that instead of f = 2π √{ k/m } it oscillates at a frequency f given by :

f = 2π √{ k/(m + q.ρ) }                              new mass of the system = m + q.ρ

where q is a constant and relates to a the volume of the gas which the oscillating system pushes to and fro as it vibrates (this volume is just a layer near to the oscillator – about as thick as the oscillator is thick from front to back – actually the gas isn’t a separate ‘solid’ layer, of course, its equivalent to gas near to the oscillator moving a lot and the gas far away from the oscillator moving much less – the integral of that movement over distance from the oscillator gives you the equivalent layer thickness. Multiply that layer thickness and area by the gas density and you have the mass that must added to the oscillator mass to give the new increased effective mass of the oscillator in a gas.

So in effect, the gas forms a surface layer around the mass, making it more massive, without significantly affecting its motion in any other way. You can get the same effect by taking a bell or a tuning fork and ringing it, and then partially immersing it in water – the frequency can be heard to go down distinctly.

Bell = oscillator

Ring it

Put it underwater

Ring it

What do you get?

f = 2p√(k/(m + q.ρ)

because water = 800x more dense than air, you get an audibly lower note

So different gases –> different relative molecular masses –> different densities –> different frequencies

So, measure frequency and you have the relative molecular mass.

Problems may arise if the temperature and pressure are different from STP. If your gas is hotter or colder than 273.15 K, or atmospheric pressure changes (or your gas is pressurised), you can correct the answer you get by using the Ideal Gas Equation:

PV = nRT

The pressure correction is:

RMM –> RMM x Po/P

where Po is atmospheric pressure, P the pressure of measurement. (These are absolute pressures, of course, not pressures relative to atmosphere, what we call in industry ‘gauge’ pressures.)

And the temperature correction is:

RMM –> RMM x T/To

where To is 273.15 K, and T the absolute temperature of the room.

The beauty of Professor Downie’s little device for measuring the relative molecular mass is that it will automatically correct for changes in temperature and pressure.

The link below gives the patent information for the device.

http://worldwide.espacenet.com/publicationDetails/biblio?FT=D&date=20120530&DB=worldwide.espacenet.com&locale=en_EP&CC=EP&NR=2458377A1&KC=A1&ND=4

www.espacenet.org will give you information about other inventions of Professor Downie.

Quartz

The device contains quartz and a quartz oscillator has some rights to be considered a Wonder of the Modern World. The quartz crystal is the most accurate device you can buy for 10 pennies – it offers parts per million time measurement you can fit on your fingernail. These little beauties are made of crystalline quartz or silicon dioxide – also known as ‘sand’. But this is sand carefully machined into plates of precise size and thickness. Quartz is one of those materials where Nature seems to have smiled. It has one of the lowest coefficients of thermal expansion of any material, so it doesn’t expand and contract with temperature. Its coefficient of temperature change of modulus – ‘springiness’ – is also one of the lowest known. And, to round off its manifold virtues, the quartz crystal is piezoelectric. Which means that if you attach a pair of wires and put an electric field across it, it shrinks – ever so slightly, but it shrinks. The piezoelectric effect works both ways, so if you squeeze, it makes a tiny flow of current flow in the wires. This in turn means that you can make a tuning fork which you can set vibrating with an electronic circuit, and detect it vibrating with an electronic circuit. Its happy combination of properties mean that a quartz crystal oscillator can be made, which can run for 20 years from a coin-sized battery, marking time to 5 parts per million or better – a couple of minutes in year.

It is a quartz crystal that is inside almost every watch and clock in the world, and all computers and phones. For a watch or clock, a crystal running at 32,768Hz is hooked up to a frequency divider, with 14 successive binary divisions giving a 1Hz signal which will run a tiny synchronous motor which turns the hands of the timepiece.

Accurate to 1 part per million (30 seconds in a year)

Quartz in an oven 1 part per 100 million

Atomic clock 1 part in 100,000 million

Used in computer clocks

The change in frequency when you put a quartz into gas, at least at ordinary pressures up to a MPa or so, is very small. Using a crystal of 32,768Hz with air at atmospheric pressure, the frequency change is only around 8Hz, for air of molecular mass 29 (the weighted average of oxygen/nitrogen/argon). But this small change is all you need to measure molecular mass. Helium will give 1Hz, Argon 11Hz, and so on; the change in frequency is simply proportional to their molecular mass.

To demonstrate his device Professor Downie had a number of balloons each filled with a different gas. Members of the audience measured the RMM of these gases and the results were collected. The device was able to identify the gas in each balloon.

Towards the end of the lecture Professor Downie demonstrated some of his other inventions.

Binary Pinball

Binary and Clocks

Computer clocks use binary.

The binary pinball is really just to show how you can use electronic binary counters to step down the frequency of an oscillator – like the ultrasonic quartz oscillators – to the 1Hz or so you need to operate an LCD watch or a mechanical watch/clock dial. The professor uses this demonstration to teach children about binary.

The pictures above show a Binary counter with marbles.

The demo moves flippers from 1 to 0 with each marble.

4 flippers mean the clock goes 0123456789ABCDEF in hexadecimal, and then resets to zero.

The demo runs from watch crystal (32768 Hz).

Divides by 2 to the power 12, twice.

Binary Clock

Quartz watch oscillating at 32.768 kHz. We divide that frequency by 2 to the power 24 (not all 24 outputs on LEDs).

The New Science of Marblonic Amplifiers

An amplifier works by taking a small input and increasing it.

To keep an oscillation going you need to have an amplifier.

One end of the oscillator is connected to the output, the other to the input of the amplifier.

How does a transistor amplifier work?

An electron goes in the base – that’s the input.

Lots of electrons come out of the emitter – from the battery or power supply of electrons.

The base and emitter electrons go down the collector.

The collector is the output: more comes out than went in.

It’s a bit like a marblonic amplifier.

Oscillators from amplifiers

Take a microphone.

Connect it up to a PA amplifier.

Connect that to a loudspeaker.

Put microphone next to loudspeaker.

SQUAAAAAAAAAWWWK !

The slightest signal, the tiniest bit of noise, is amplified.

This comes out of the speaker.

This goes in the microphone.

It gets amplified again and comes out of the speaker.

It goes in the microphone again even bigger….

And so on… It’s a recursive process.

The Saxotron

Microphone

Loudspeaker

Pipe

Amplifier

You know what’s going to happen…

Slide the telescoping pipes to and fro to produce different notes.

Different harmonics if you slide too far.

Sounds a bit like it was a cross between: a saxophone and a swanee whistle a trombone and a clarinet.

Two crystals meters and Beat frequencies

In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies.

http://en.wikipedia.org/wiki/Beat_(acoustics)

Use two crystals, one in vacuum, and the other in gas and measure the beat frequency.

Beat frequency reduces the frequency so that small changes are relatively bigger.

fo (frequency of crystal in vacuum) = 32768 Hz approx

fair (frequency of crystal in air) = 32760 Hz approx

Need a precise frequency meter

BUT

∆f = fo – f(air) = 8Hz

Easy to measure on a simple, low cost, not-very-accurate multimeter.

Beat frequencies

Beat frequencies with XOR gate

SYNC: oscillator coupling problems

It’s a bit like two pendulums on string. One picks up energy from the other

Then gives it all back again

Active oscillators do it differently.

If VERY close in frequency, they tend to lock together. You can choose to offset the zero

àH2 & low pressures work better

Filtering Frequencies

Low pass filters

Car silencers: narrow pipe, then reservoir volume, then narrow pipe, then reservoir…

Electronic RC filters

R – resistor (narrow pipe)

C – capacitor (reservoir)

Discovery of elements by spectra

Helium, Europium, Indium, Thallium, Caesium, Rubidium were discovered when looking at their optical spectra. Helium was seen in the spectrum from the Sun. The others were seen when burnt in a Bunsen flame.

Discovery of Argon

http://www.chem.ucl.ac.uk/resources/history/chemhistucl/hist14.html

Nitrogen from different sources was found to have different densities.

On April 19th 1894 Ramsay heard Lord Rayleigh lecture to the Royal Society, when he pointed out that nitrogen isolated from the air had a density slightly higher than that of nitrogen prepared from chemical sources. A litre of pure nitrogen gas generated from a chemical reaction weighed 1.2505 g. On the other hand, a litre of nitrogen gas generated from air by removing oxygen, carbon dioxide, and water vapour weighed 1.2572 g (at the same temperature and pressure). Rayleigh thought that this might be due to the presence of a light impurity in the former.

Above right: https://en.wikipedia.org/wiki/William_Ramsay

But Ramsay thought that it might be due to the presence of a heavy impurity in the ‘atmospheric’ nitrogen. He was an enthusiast for the Newland/Mendeleev Periodic Table. He thought that there might be an unrecognised new element hiding in the air, and that there might be room for this in a new Group at the end of the Periodic Table.

When examinations had finished, Ramsay set about attempting to isolate this ‘impurity’.

He repeatedly passed nitrogen from the air over red hot magnesium, which reacted to form magnesium nitride, and as the volume decreased, the density rose. 22 Litres of the gas with a density of 14 were reduced to 1.5 l with a density of 16.1, and then finally to a residual 290 cm 3 with a density of 16.1 and then to 290 cm3 with a density of 19.95, and which would no longer react with magnesium. Measurement of the specific heat showed it to be monatomic, and therefore the atomic weight was 39.9, and it fitted into the Periodic Table between chlorine and potassium as the first member of a new Group. With the advice of a colleague from the Classics Department, he called this gas argon, after the name argon given in the Greek Old Testament to describe ‘the workers who stand idle in the market place’

Below is a picture of the historic vessel for doing this which can be found outside the Royal Institution theatre in London.

Argon discovery led William Ramsay directly to the distillation of Liquid air and thence to Ne, Kr, Xe.

Professor Downies’ hands-on-real-stuff philosophy

It’s always worth doing the experiment, building the project, seeing and feeling the real world.

Stuff you can get your hands on you believe.

Stuff you can get your hands on you remember.

There are always extra things to learn.

Subtleties, second order effects.

Failures (= “prototypes”) nearly always teach your something

Expect The Unexpected !