Gold Nuggets in 2019

Between 1850 and 1900, the city of Bendigo in Victoria, Australia, was the centre of a Gold Rush. Central Deborah Gold Mine, the last commercial gold mine to operate in Bendigo, re-opened as a tourist attraction in 1986.
Gold can still be found in the Bendigo area.
On Mothers' Day 2019, a family out walking Lucky their dog on the outskirts of Bendigo walked onto a gold nugget. They took it along to the local IGA supermarket to weigh it. The gold nugget weighed 624 grams (about 20 ounces).
Today, the price of gold in Australia is listed as $65.76 per gram. So, if pure, the gold in this nugget would be worth 624 × $65.76 ≈ $41,000.
How big would this gold nugget be?
We know the mass of the nugget is 624 grams.
We can look up the density of gold in tables, ρ = 19.3 g cm^-3
Since density = mass (g) ÷ volume (cm³)
19.3 = 624 ÷ volume (cm³)
volume (cm³) = 624 g ÷ 19.3 g cm^-3 = 32.3 cm³
Which could be represented by a cube approximately 3.2 cm × 3.2 cm × 3.2 cm
Not very big at all is it!

Ballarat, another Victorian Gold Rush town and site of the historic "Eureka Stockade", was also the place where another spectacular gold nugget was found in June 2019 (and reported nationally in July 2019). This gold nugget weighed about 2 kilograms, or 2,000 grams.
At today's prices, it would have a value of about 2,000 × $65.76 ≈ $130,000
And how big would this nugget be?
density = mass (g) ÷ volume (cm³) volume (cm³)
density = mass (g) ÷ density (g cm^-3) = 2,000 g ÷ 19.3 g cm^-3 = 103.6 cm³
The dimensions of a cube with this volume would be about 4.7 cm × 4.7 cm × 4.7 cm
Which would fit nicely into the palm of your hand as shown in the photograph below

Further Reading:
Density Calculations

Suggested Study Questions:

1.  The density of gold is 19.3 g cm^-3. Calculate the mass of
   • 1 cm³ of gold 
   • 10 cm³ of gold 
   • 1 m³ of gold
2.  The density of gold is 19.3 g cm^-3. Calculate the volume of
   • 1 g of gold
   • 10 g of gold
   • 1 kg of gold 
3.  The density of gold is 19.3 g cm^-3. Calculate the dimensions of a cube of gold which has a mass of
   • 5 g
   • 500 g
   • 5 kg
4. The density of gold is 19.3 g cm^-3. Calculate the diameter of a sphere of gold which has a mass of
   • 2 g
   • 200 g
   • 2 kg
5. A credit card has the approximate dimensions 65 mm × 55 mm × 1 mm. Calculate:
   • volume of the credit card in cm³
   • mass of a gold credit card
   • value of a gold credit card if the cost of gold is $65 per gram
   • Why aren't "gold" credit cards really made out of gold?
6. Gold is one of the few metals that is found in nature as the "native" element (that is, it is found as the element and not in compounds). Explain why gold can be found in nuggets.
7. Name some other metals that can also be found in their native state (that is, found as the element and not as compounds). Explain why these metals can be found in their native state. 
8. Name a metal that is not found on Earth in its native state, and explain why it is not found in nature as the uncombined element.

Spud Lite?

"Spud Lite", the advertising poster said, "25% less carbs", followed in fine print by "than other potatoes".
"How strange", I thought, "I thought you ate potatoes for their carbohydrate (carbs) content so why would you want a potato with less carbohydrate?"
But then I started thinking about what this meant in terms of the chemical composition of the potato. If it contains 25% less carbohydrate, then surely that means something else must have been increased or added? Or are you just getting less potato for your money?

Typically, a traditional potato has the following approximate composition:

nutrient	% by mass
water	79
carbohydrate	17.5
protein	2
fat	0.1

 That is, 100 g of traditional potato contains about 79 g of water, 17.5 g of carbohydrate, 2 g of protein and 0.1 g of fat.

One way to reduce the percentage of carbohydrate in a potato would be to reduce the density of the potato.
If 100 g of a traditional potato had a volume of 92 mL, then the density of the potato would be 1.09 g/mL. 1 mL of traditional potato has a mass of 1.09 g and contains 17.5% by mass (0.19 g) of carbohydrate.
If "spud lite" has a lower density of potato "flesh", say 0.8 g/mL, then 1 mL of "spud lite" has a mass of 0.8 g and contains 17.5% by mass (0.14 g) of carbohydrate.
If we then compare equal volumes (sizes) of potatoes, say 1 mL of traditional potato and 1 mL of "spud lite" we find that "spud lite" contains 100 x (0.19 - 0.14)/0.19 = 26% less carbohydrate (by volume!).
But, if the density of "spud lite" is less, the % by mass composition remains the same, that is, for every 100 g of potato (traditional or "spud lite") there will be 17.5 g of carbohydrate (but the "spud lite" potato will be a bigger potato for your 100 g).

The nutrition label on a packet of "spud lite" potatoes gives the following masses per 100 g of potato:

• fat < 0.1 g
• protein 1.4 g
• carbohydrate: 8.9 g
• sugars: 1.1 g
• dietary fibre:  1.4 g

So, the total carbohydrate content is 8.9 + 1.1 + 1.4 = 11.4 g
(assuming the dietary fibre is cellulose which is also a carbohydrate).
This means that the actual mass of carbohydrate per 100 g of potato has been decreased. That is, "spud lites" are not just less dense than traditional potatoes.

 Another way to decrease the proportion of carbohydrate in your potatoes would be to increase their water content.
Imagine you have 100 g of traditional potato. This potato is made up of 79 g of water and 17.5 g of carbohydrate.
"Spud lite" contains 11.4 g of carbohydrate.

If all the lost mass of carbohydrate in the "spud lite" (17.5 - 11.4 = 6.1 g) was present as water, then the mass of water in "spud lite" = 6.1 + 79 = 85.1 g

And you, the consumer, is just paying for additional water in your potato!

Further Reading
 Experimental Design

 Carbohydrates
Proteins
Lipids (fats and oils) 
Percentage Composition
Density 

Suggested Study Questions:

1. Design an experiment to test the hypothesis that "spud lite" potatoes have a lower density than traditional potatoes.
2. Design an experiment to test the hypothesis that "spud lite" potatoes have a greater percentage by mass of water than traditional potatoes.
3.  For each serving of traditional potato given below, calculate the mass of carbohydrate consumed:
• 25 g of potato
• 75 g of potato
• 135 g of potato
4. Calculate the mass of "spud lite" you would have to consume in order to obtain
   • 1 g of carbohydrate
   • 7 g of carbohydrate
   • 21 g of carbohydrate
5. The density of potato changes as the potato ages on the shelf. The table below shows the results of an experiment in which the mass and volume of the same potato is measured and recorded every 3 days. Calculate the density of the potato on each day.

   Day	Mass (g)	volume (mL)
   1	142	130
   4	140	129
   7	138	128

6. Consider the results of the experiment above. Describe any trends that you see in the data and suggest reasons for these trends.
7. Explain what chemists mean when they refer to "carbohydrates".
8. The nutrition label on "spud lites" lists the mass of carbohydrate, sugars and dietary fibre separately. What do you think the "carbohydrate" is on this label?
9. Add together the percent by mass of all the components listed for a traditional potato.Suggest reasons for why the total percentage is less than 100%.
10. Potatoes are usually classified as high on the glycemic index (GI). What does this mean?

Lucapa Diamond

The Perth-based Lucapa Diamond Company found a 404 carat diamond at its mine in Angola, a republic in southern Africa. It is the biggest diamond found to date in Angola and has been valued at about $20 million.

The mass of gemstones such as diamonds is measured in carats. 1 carat equals 200 mg.
1 carat is subdivided into 100 points, so a point is equal to a mass of 2mg.

Diamonds form at depths of 150 - 200 km in the upper mantle where temperatures range from 900 to 1300^oC and the pressure is about 50,000 times atmospheric pressure. Under these extreme conditions, carbon atoms come together to form the diamond structure in which each carbon atom makes 4 covalent bonds to other carbon atoms. In the diagram shown, each black ball represents a carbon atom and each line represents a covalent bond.

Diamonds are brought to the earth's surface from the upper mantle  in a dyke which geologists refer to as a kimberlite pipe.

 The density of naturally occurring diamonds varies between 3.15 and 3.53 g cm^-3, with the purest diamonds having a density closer to 3.52 g cm^-3.
Type I diamonds include diamonds in which nitrogen is present as an impurity. A colourless Type 1 diamond has very little nitrogen impurity. As the amount of nitrogen present increases, the diamond becomes more yellow.
Type II diamonds have  no measurable nitrogen impurity. The Lucapa diamond is a Type II diamond and is colourless because it contains no measurable nitrogen or other impurity, and, the structure has not been changed significantly from the "pure" diamond structure shown above during formation.
Some Type II diamonds are coloured pink, red or brown as a result of changes to the structure of the diamond during formation so that light is scattered in such a way as to produce these colours.
The presence of boron as an impurity results in a light blue coloured diamond, whereas the presence of black impurities such as graphite or sulfides produces a black diamond.
The presence of measurable quantities of hydrogen as well as structural changes during formation can result in purple diamonds.


Reference:
http://www.abc.net.au/news/2016-02-15/giant-diamond-found-in-angola-by-wa-company-lucapa/7168974


Further Reading:
Mass Conversions
Density
Allotropes


Suggested Study Questions:

1. Convert 200 mg to a mass in
   • grams
   • kilograms
   • micrograms
2. The diamond found at Lucapa is reported to be a 404 carat diamond. What is the mass of this diamond in
   • grams
   • kilograms
   • micrograms
3.  The value of the Lucapa diamond is estimated to be $20 million. What is the value of the diamond:
   • per carat
   • per point
   • per milligram
   • per gram
4. Assuming the Lucapa diamond to be a pure diamond, its density is 3.52 g cm^-3 . What is the volume of this diamond? 
5. Imagine pouring 500 mL of water in a 1000 mL measuring cylinder at 101.3 kPa and 25 ^oC, then dropping the Lucapa diamond into the water. What would the new volume of water be in the measuring cylinder? (assume the density of water is 1 g cm^-3)
6. Coal is also made up largely of carbon atoms, with tiny amounts of oxygen and impurities such as sulfur.  It is usually found as a vein or seam of coal within sedimentary rocks. Coal has an average density of about 1.2 g cm^-3. If a lump of coal had the same volume as the Lucapa diamond, what would its mass in grams be?
7. Given the difference in the density of diamond and the density of coal, what does this tell you about the structure of diamond and coal?
8. If you were given 5 grams of coal and 5 grams of diamond, which would have the greatest volume?
9. Draw a diagram to represent the 3-dimensional structure of diamond. On your diagram:
• draw a red line to indicate a covalent bond
• use a blue pencil to show a carbon tetrahedron
• use a black pencil to show one carbon-carbon bond angle
10. What is the angle between two adjacent carbon atoms in the diamond structure?

Packing Density

In the particle theory of matter, all matter is made up of tiny particles. You've probably drawn circles in boxes to represent solids, liquids and gases. Each of those circles is a 2-dimensional representation on the paper of a 3-dimensional sphere. So, your representation of the particle theory of matter also implies that all matter is made up of particles which are spherical in shape.

If you draw the circles so close to each other that they are touching, you label the drawing "solid".
If the circles are little bit further apart, you label the diagram "liquid".
If the circles are much further apart, you label the drawing "gas".
But, have you ever wondered just how close you can pack those spheres together?

The study of soot is becoming very important because soot in the air relates to the balance of climate: heating from light absorption versus cooling from light reflection.
Soot is made up of small round particles of carbon about 10 or 20 nanometres across. The particles stick together randomly in short chains and clumps of a half dozen or more spheres. These, in turn, clump loosely together to form larger, loose aggregates of 10 or more which over a few hours will compact into a somewhat tighter ball which is atmospheric soot.
The closer you pack the soot spheres together, then the more dense the soot becomes. That is, since all the atoms have the same mass, if you pack them more tightly together then they will occupy a smaller volume, and, since density is mass per unit volume, the density of the soot will increase.

Mathematicians have been looking at sphere packing problems for more than a hundred years. In 1831, Carl Friedrich Gauss (one of the greatest mathematicians the world has known), determined that a close-packed arrangement in which 1 sphere is surrounded by 12 other identical spheres has an average density of π/√18 ≈ 0.74
The assumed density of soot in models of atmospheric soot has, until now, been 0.74.

A research group at the National Institute of Standards and Technology (NIST), have made measurements of actual soot particles and found the density of soot to be 0.36 not 0.74
So, the researchers set out to model soot particles using 6 mm plastic spheres glued together in thousands of random combinations forming clumps of from 1 to 12 spheres which were then used to fill every available size of graduated cylinder. When they graphed their results as a function of clump size,  they got a curve which levelled off at 0.36, the same as the density of soot particles they measured, but not the same as that predicted by the close-packing of spheres according to Gauss.

It now appears that, under normal conditions (not extreme temperature or pressure), the density of close-packed particles of any size, from nanometres to tens of metres is 0.36

Reference:
C. D. Zangmeister, J. G. Radney, L. T. Dockery, J. T. Young, X. Ma, R. You, M. R. Zachariah. Packing density of rigid aggregates is independent of scale. Proceedings of the National Academy of Sciences, 2014; DOI: 10.1073/pnas.1403768111


Further Reading
http://ausetute.com.au/density.html
http://ausetute.com.au/massconv.html
http://www.ausetute.com.au/voluconv.html

Suggested Study Questions

1. Draw a diagram to represent each of the following states of matter using the particle theory of matter:
   • solid
   • liquid
   • gas
2. Calculate the volume of a spherical carbon particle that is 20 nanometres in diameter.
3. Calculate the volume of a cube in which the length of each side is 20 nanometres.
4. Calculate the ratio of the volume of the sphere to the volume of cube.
5. Why is this ratio NOT 0.74?
6. Draw a diagram showing the close-packing of just 2 carbon particles each with a diameter of 20 nanometres.
7. Draw a square around each sphere to represent the volume of space occupied by the close-packed spheres and label the total volume occupied and the volume of carbon particles.
8. For the close-packing of 2 carbon particles as drawn above, calculate the ratio of the volume occupied by the spheres to the total volume of the rectangular prism.
9. Consider placing 1 more sphere above the 2 spheres you have already drawn. Draw a diagram of an arrangement that will occupy the
   • maximum total space
   • minimum total space
10. Research the difference between hexagonal close packing and cubic close packing.

Methanol and the Home-Brewer

In June 2013, a young man in Queensland died as a result of drinking homemade liquor. It is believed that the liquor contained a toxic level of methanol (also known as wood alcohol). Drinking 10 mL of pure methanol can cause permanent blindness, drinking 30 mL of methanol can kill you.

The first step in the production of homemade liquors, is the fermentation of sugar.
Methanol, CH₃OH,is formed during fermentation.
When fermenting 6 kg of sugar dissolved in water for the production of distilled spirits such as whiskey or vodka, the home-brewer (and home-distiller) will typically find that the concentration of methanol in their brew is about 3 parts per million.

Many fruits are used by the home-brewer as the source of sugar to be fermented. Each fruit will lend a distinctive flavour to the final product. But fruits that are high in pectin will produce greater concentrations of methanol. Apples, apricots, guavas, quinces, plums, gooseberries, and citrus fruits like oranges, all contain high levels of pectin, typically more than 1% by mass pectin. Grapes, cherries and strawberries contain low levels of pectin, less than 1% by mass pectin.

Pectin contains  galacturonic acid which has the structural formula shown below:

In pectin, about 80% of the carboxyl groups in galacturonic acid are esterified with methanol. The remaining non-esterified carboxyl groups exist as the acid, or as salts with sodium, potassium or calcium. When pectin is broken down by enzymes during the brewing process, the methyl esters react with water to produce methanol.

The second step in the production of homemade liquor is the distillation step.
This is the crucial step in removing as much of the toxic methanol as possible.
The boiling point of methanol is about 65^oC, but the boiling point of ethanol (the desired product) is about 78^oC. During the distillation process, the first fraction collected should contain the methanol. This fraction should be collected and discarded. The next fraction should contain the desired liquor. It is highly recommended that any distillate collected after about 96^oC also be discarded.


Reference:
http://www.couriermail.com.au/news/queensland/ballandean-man-bill-lynam-who-lost-his-son-joel-to-homemade-liquor-poisoning-is-thankful-that-other-son-joshua-survived/story-fnihsrf2-1226664893229

Further Reading
http://ausetute.com.au/members/alkanolp.html (members only tutorial on alkanols)
http://ausetute.com.au/members/carboxyl.html (members only tutorial on alkanoic acids) 
http://ausetute.com.au/partspm.html 
http://ausetute.com.au/density.html 

Suggested Study Questions:

1. Draw the structural formula for methanol.
2. Locate the functional group present in methanol on the structural formula above. Name the functional group. 
3. At 25^oC methanol has a density of  0.79 g mL^-3. Calculate the mass of methanol present in a lethal dose of pure methanol .
4.  Convert the concentration of methanol given for homemade whiskey into a concentration in g mL^-1.
5. Assume the young man who died drank homemade whiskey. What minimum volume of homemade whiskey did he drink?
6. For galacturonic acid given the:
   • molecular formula
   • molar mass
7.  On the structural formula for galacturonic acid identify and name the functional groups present.
8. Draw the structure for the sodium salt of galacturonic acid.
9. Draw the structure for galacturonic acid esterified with methanol.
10. Give the molecular formula and molar mass for the structure above.
11. Apples contain about 1% by mass pectin. 10 kg of apples are to be used in the production of a homemade liquor. What mass of pectin will be present?
12. Assume exactly 100% of the carboxyl groups in galacturonic acid are esterified with methanol. How many moles of the ester are present in 10 kg of apples?
13. Write an equation representing the reaction between this ester and water to form methanol  and galacturonic acid.
14. How many moles of methanol could be produced by the break down of pectin in 10 kg of apples?
15. Assuming the young man who died had drunk this apple concoction without distilling and removing the methanol, what minimum volume of fermented apple-drink would he have had to have drunk?
16. Why do you think most countries have outlawed home-distilling?

World's Lightest Material?

UC Irvine, HRL Laboratories and the California Institute of Technology have announced that they have succeeded in making the world's lightest material, with a density of 0.9 mg/cm³.

This material is made up of a metallic lattice of interconnected hollow tubes with walls a thousand times thinner than a human hair. Because of this open lattice structure, the material is actually made up mostly of air, 99.99% air .

But what is the metal making up this new material?

We know the density of the new material, so we can calculate the mass of a 1cm cubed volume of this material:

1cm³ of the new material would have a mass of 0.9 mg = 0.0009g.

If 99.99% of the mass of this material is made up of air, then

the mass of air = 99.99/100 x 0.0009 = 8.991 x 10^-4g (0.8991 mg)

and the mass of metal in the new material = 0.0009 - 8.991 x 10^-4 = 9 x 10^-7g (9 x 10^-4 mg)

If we assume that 0.00001% of the volume of the new material is metal, then

the volume of metal = 0.00001/100 x 1cm³ = 1 x 10^-7cm³

So, the density of the pure metallic solid would be 9 x 10^-7g/10^-7cm³ = 9g/cm³

If we compare this calculated density of the metal to a list of common metals as shown below,

Pure Substance	State	Density (g/cm3) at 25oC and 1atm
gold	solid	19.3
mercury	liquid	13.6
lead	solid	11.4
silver	solid	10.5
copper tin	solid solid	9.0 7.3
zinc	solid	7.1
aluminium	solid	2.7

then we see it is possible that the new material is made up of copper.

Reference

T. A. Schaedler, A. J. Jacobsen, A. Torrents, A. E. Sorensen, J. Lian, J. R. Greer, L. Valdevit, W. B. Carter.Ultralight Metallic Microlattices. Science, 2011; 334 (6058): 962 DOI: 10.1126/science.1211649

Further Reading

Density Calculations

Suggested Study Questions

1. Using the table of densities above, calculate the mass in grams of a
   • cubic centimetre of gold
   • a cubic metre of copper
   • a cubic millimetre of silver
   • a cubic kilometre of zinc
2. Using the table of densities above, calculate the volume in cubic centimetres of
   • 1g of copper
   • 100mg of lead
   • 4500μg of aluminium
   • 2kg of silver
3. Brass is a mixture of copper and zinc. A sample of brass has a density of 8.5g/cm³
• What is the mass a cubic centimetre volume of this brass sample?
• If the sample were made up of equal masses of copper and zinc, what is the mass of copper in the sample?
4. A sample of brass was produced using 500cm³ of each of copper and zinc.
• What mass of copper is present in the brass?
• What mass of zinc is present in the alloy?
• Assuming additivity of volumes, what is the density of this brass sample?
5. Cymbals are commonly made of bronze which is a mixture of about 10% (by mass) tin and 90% (by mass) copper. For a 100g sample of bronze, calculate
• the mass of copper present in the sample
• the volume of copper this mass represents
• the mass of tin present in the sample
• the volume of tin this mass represents
• the density of the bronze sample assuming additivity of volumes
6. Typically, bronze contains copper and about 12% (by mass) tin. Calculate the density of a sample of this bronze.
7. Bronze coins often contain copper and about 5% tin. Calculate the density of the bronze used to make coins.
8. The brass used to make springs and screws is often 65% (by mass) copper and 35% (by mass) zinc. Calculate the density of the alloy in a brass screw.

Bone Composition

Bone is a kind of specialized connective tissue providing a supportive framework for the body. Bones are continually being remodeled during the life of the body so they can be used to determine the age of a body.

About 70% of bone is made up of calcium hydroxyapatite, 3Ca₃(PO₄)₂.Ca(OH)₂.
The crystals of calcium hydroxyapatite in bone are very small, about 5nm x 5 nm x 40nm.
The total surface area of calcium hydroxyapatite in bone is extremely large, about 40 hectares in the skeleton of a 70kg man.
About 10% of bone is made up of water, and the other 20% is made up of organic compounds such as collagen. The term collagen refers to a group of proteins, and is the most abundant protein found in mammals, about 30% of all the protein in the body is collagen.

The bone of very young people, less than 4 years of age, is called woven bone because the collagen fibres are interwoven and run in all directions just like a piece of felt, and the bone contains large holes like Swiss cheese.

The bones of bones of adults include lamellar bone which has collagen fibres organized into layers or sheets known as lamellae. These are usually built up around blood vessels like the layers of an onion. This produces compact bone.
Adult bones also include trabecular (cancellous, spongy) bone. The bone itself is in the form of little beams (trabeculae) which are about 200μm thick. The spaces in the bone can contain marrow.

Osteoporosis refers to a decrease in the amount of bone tissue which results in an increased tendency for the bone to fracture. The shape and size of the bone doesn't change, but the little beams, the trabeculae, become thinner and some may disappear altogether.
Astronauts in space can also display a decrease in the amount of bone tissue because there is less load, and therefore less stress, on their bones in space.

Aerobic and resistance training increase the density. Bone is deposited when there is load, and stress, applied to the bone.

Scientists at the Rensselaer Polytechnic Institute have developed a new technique to analyze the bone matrix. This technique provides information about the concentration of different proteins in the bones, which can be used to determine how the bone was formed, how it has been modified over time, and, if the bone is prone to fracture.

Reference
G. E. Sroga, L. Karim, W. Colon, D. Vashishth. Biochemical characterization of major bone-matrix proteins using nanoscale-size bone samples and proteomics methodology. Molecular & Cellular Proteomics, 2011; DOI: 10.1074/mcp.M110.006718

Further Reading
Molecular Mass (Formula Weight)
Percentage Composition
Unit Conversions
Density
Mass-Mole Calculations

Study Questions

1. Calculate the molecular mass (formula weight) of calcium hydroxyapatite.
2. Calculate the percentage composition of calcium hydroxyapatite.
3. 1 hectare is 1,000m², what is the surface area in m² of calcium hydroxyapatite crystals in a 70kg man?
4. If you laid out all the calcium hydroxyapatite crystals in the bones of the 70kg man above onto a football field, how many football fields would you need? (Assume a football field is about 6,000m²)
5. The little beams in trabecular bone are 200μm thick. Convert this to a thickness in
   
   • meters
   • millimeters
   • nanometers
   • angstroms
6. The density of a bone in the leg is about 2g/cm³. 70% of bone is made up of calcium hydroxyapatite. Calculate:
   • the mass of calcium hydroxyapatite present in a 500cm³ bone sample
   • the moles of calcium hydroxyapatite present in the same bone sample
   • the percentage of calcium present in the same bone sample
   • the mass of calcium present in the same bone sample
   • the mass of water present in the same bone sample
   • the mass of organic compounds present in the same bone sample
     
7. Which type of bone, woven bone or lamellar bone, has the greatest density? Explain your answer.
8. Will the bones of a person suffering from osteoporosis be more or less dense than the bones of an athletic young adult? Explain your answer.