Archimedes’ Dilemma
Date: _______________
Name: ___________________________ WS#
Color: ______________________
Directions: Read the passage below and answer the questions that follow.
Suppose you were given two glasses of a clear liquid substance and were told that one contained water and the other contained a deadly acid. You were then challenged to figure out which glass was safe to drink at the end of two hours. You would certainly want to be sure you made the right choice.
The same type of challenge was presented to a scientist named Archimedes in the first century B.C.E., except the life at stake was not Archimedes, but a goldsmith who been commissioned by King Hiero to make a gold crown. The king was not a trusting man. He questioned whether the today he would have known that matter has characteristic properties. He could have identified the gold by its characteristic properties.
A characteristic property is a unique trait of a substance that never changes and can be used to identify the substance.
Some characteristic properties include the following: the melting point, or when a solid changes to a liquid; the boiling point or when a liquid changes into a gas; density, or the ratio that compares the volume and the mass of a substance to relate how much matter is in a space; and goldsmith had replaced some of the gold with silver. He challenged Archimedes to solubility, or the amount that will dissolve in another substance. answer the question. Had Archimedes live
Groups of substances have characteristic properties that help you identify them as a group member. Examples of some of these groups and their characteristic properties are shown in the table below.
Group
Acids
Bases
Metals
Nonmetals
Solids
Liquids
Gases
Characteristic Properties
Sour, react with metals and carbonates, turn blue litmus paper red
Bitter, feel slippery, and turn red litmus paper blue
Shiny, good conductors of heat and electricity, a flexible and able to bend without breaking, exist as a solids, high melting point, react with acids
Dull, poor conductors of heat and electricity, brittle and cannot bend without breaking, have low melting points
A definite volume, fixed shape
A definite volume, takes the shape of the container they are in
No definite volume or shape
Archimedes thought about the king’s question for several days. During this time, he didn't eat, sleep, or bathe. It is said that he began to smell so bad that one of his neighbors suggested
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that he take a bath. Archimedes relented. The story goes on that once he stepped out to bathe and fully immerse himself, he quickly got out and ran through the streets explaining, “Eureka!
I’ve found it!” He went home and tested the crown and was able to inform the king that the goldsmith was indeed dishonest. How Archimedes solve his dilemma is revealed an experiment that follows.
Archimedes’ Question: How can I prove that the king’s crown is pure gold?
Archimedes’ Hypothesis: if the crown is pure gold, but it will displace the amount of water and a basin equal to the displacement of the same weight in gold.
Materials: King’s crown, equal amounts of gold as given to the goldsmith, equal weight of silver, a large basin, water
1.
Fill a large basin almost full with water, and measure the level of water.
2.
Place the gold (as given to the goldsmith) in a basin of water.
3.
Measure the level of water in the basin with the gold added.
4.
Find the difference between the two levels to determine how much water has been to this place. Remove the gold.
5.
Measure the level of water in the basin again.
6.
Place the silver in a basin of water.
7.
Measure the level of water in the basin with the silver added.
8.
Find the difference between the two levels to determine how much water was displaced.
9.
Remove the silver. Then measure the level of water in the basin again.
10.
Place the crown in the basin of water.
11.
Measure the level of water in the basin with the crown added.
12.
Find the difference between the two levels of water to determine how much water was displaced.
13.
Carefully remove the crown.
14.
Repeat the experiment to make sure and innocent man is not beheaded.
Archimedes’ Conclusion: Based on the experiment, the king’s crown displaced a smaller volume of water and pure gold; therefore, the crown is not pure gold.
Archimedes Inference: The king’s crown was a combination of gold and silver because it displaces amount of water somewhere between the displacement of the gold and the silver.
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Archimedes earned a place in your science book because he developed a procedure used today to find the volume of any irregularly shaped object, such as a crown. Volume is a measurement of the amount of space something takes up. When you place the object into the water, the level of water rises as the water is displaced, or moved out of the way. To find the volume of an object you simply need to find the difference between the level of water with the object in it and its beginning level.
Had Archimedes been able to measure the mass of the gold, he could have found its density.
Mass is a measurement of how much matter, or stuff, is in an object. Density compares mass and volume to determine how much matter is packed into a given amount of space.
The density of gold is 19.3 g/cm³. This means that for every cubic centimeter – about the amount of space and unused eraser at the end of a pencil takes up – there are 19.3 g of gold – about the same amount of stuff you’d find in 19 plain candy-coated chocolate candies. Since the candy takes up more volume, it is less dense.
Gold is very dense, meaning that the atoms that make up gold are very close together. On the other hand, silver is less dense, having a density of 10.5 g/cm³. No matter how much or how little gold or silver one has, the density of each will remain the same.
Another characteristic property is related to the how gold and silver react to heat. If
Archimedes had been able to melt down the crown – turning it from a solid to a liquid – he could have measured its melting point and answer the king’s question. However, he didn’t know that gold has a boiling point of 1064°C and that silver has a lower melting point of
961.78°C. He could have attempted to vaporize the crown, turning it from a liquid to a gas – and find its boiling point. This would have required a great deal of heat, as the boiling point of gold is 2807°C and that of silver is 2162°C. Melting point and boiling point are both characteristic properties.
Both silver and gold are metals. This means they share the characteristic properties of other metals, as shown in the table on page
14. All metals react with acids. However, different acids affect metals in different ways. For example, silver can be dissolved and sulfuric acid, but gold cannot. Had Archimedes known this, he could have tested the crown in sulfuric acid to see what happened. He would have been testing the crowns solubility. Solubility is a characteristic property that measures how much substance will dissolve in another substance.
1 cm 3 Silver
1 cm 3 Gold
Same volume of Silver and Gold in a weighing scale
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Define: Use the reading to define the following terms in your own words.
1.
Characteristic property: _______________________________________________________
2.
Density: ____________________________________________________________________
3.
Solubility: __________________________________________________________________
4.
Mass: ______________________________________________________________________
5.
Volume: ___________________________________________________________________
Recall and Evaluate: Use the reading and your definitions to answer the following questions in complete sentences.
1.
Why can we use characteristics properties of a substance to identify it?
2.
Lacey had a shirt that looked black in the house, dark blue if she went outside and greenblack when she was under fluorescent light. Would the color of Lacey’s shirt be a characteristic property of her shirt? Why or why not?
3.
Physical property is a trait or in attributes such as size, shape, color, texture, taste, smell, or sound can be identified through observation. How does a physical property differ from a characteristic property?
4.
Identify the following properties of gold as physical or characteristic.
Property
A. Is usually yellow in color
Type of Property
B. Has a melting point of 1064°C
C. Is a shiny metal
D. Has a density of 19.3 g/cm³
5.
How can we use characteristic properties to group different kinds of matter together?
6.
What observation did Archimedes make in the bathhouse that led him to answer the king’s question?
7.
The density of a substance is related to how close its particles are together. Defined density, we need to measurements: mass and volume. What is mass? What is volume?
8.
What does it mean when we say that gold has a density of 19.3 g/cm³?
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