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Name: Colin
Status: educator
Grade: 6-8
Location: CO
Country: USA
Date: Winter 2011-2012


Question:
Is it true that the density of each substance is unique? (That is my understanding.) So when my students ask, will a substance with a density of 1g/cc float or sink in water, I should tell them that this is a highly unlikely situation because pure, distilled water is the only known substance with that density?



Replies:
Hi Colin,

No, the density of a substance is not a unique property of the substance. Density is not enough to uniquely identify a solid or liquid. It certainly is one of several physical properties that one likes to measure in order to be sure that a substance is what one supposes it to be.

Consider carbon. In its graphitic form a sample of carbon will have a density of about 2.2. In the form of diamond, carbon's density is about 3.5. This simple example shows that the manner in which the element is formed results in a phase with a very different density. More generally, one can form various minerals with various densities and there is no guarantee that one of those will not have a density of 1. The same is true with liquids - thousands of new compounds are synthesized every year, and I am willing to bet any money that some of them have a density of 1 g/cc.

It is important to realize that all measured properties, including density, have uncertainty in their determination. So when we say two substances have different densities, what we really mean is that their densities are different enough for us to be able to tell the difference. Sometimes this is not the case and you might have a substance with density very close to 1 g/cc. For example, the density of pure acetic acid at 25C is 1.049 g/cc, whereas the density of water at this same temperature is 0.998 (the density of pure water is 1.00 at 4 C). Only very accurate measurements could tell the difference between them. But of course, water and acetic acid are miscible, i.e., they readily form a mixture - so the question of what will float and what will sink is a moot point. If you combined them, yo would see only a single uniform phase.

Finally, all substances' densities change with temperature. Most substances expand as they get hotter so their density goes down, but water rather unusually increases its density from 0C to 4C and then the density decreases as temperature increases. Have a look around the web at "water density temperature" and you will see much data.

So, do not tell your students that water is the only substance with a density of 1 g/cc - tell them that the density is one of several ways we can identify water, and that 1 g/cc is an approximate value.

best, dr. topper


Hi Colin,

It depends on what you mean by "unique". If you mean that since water has a density of 1g/cc, then no other substance can have the same density, then.... no, that is not correct.

Each particular substance under well defined conditions of temperature, pressure, and perhaps one or two other criterea, will have a defined density.

There are undoubtably some other substances that happen to have a density of 1g/cc. The characteristic of density is not mutually exclusive.... just because one substance has a particular density, does not mean that some other substance cannot also happen to have that same density too.

In answer to your other question, suppose you blended a mixture of plastics to have a density of exactly 1g/cc and carefully inserted it in a water bath without pushing it. Since it would have the same density of the water around it (that is, it would have "neutral buoyancy"), it would neither sink nor rise. Wherever you carefully placed it, it would remain motionless.

Regards, Bob Wilson


Colin,

No, it is not true that the density of substances are unique for that substance. In fact, the density of substance can change as a function of temperature and pressure, so the density of a substance is not even a single number for that one substance. it can even happen that the density of a liquid can change as a function of column height - that the density of a liquid within a tall column is different depending on at what height in the column you measure.

One of the ways to measure the density of some plastics, for example, is to develop a column of fluid, drop a bead of plastic in this column, and where the plastic bead stops, the density of the liquid at that height is the density of the plastic bead. So here is an instance where we expect two different substance to have the same density.

Having said that, this could be a teachable moment. I looked up some density data on elements, and at 100KPa and 0degC, the density of carbon is listed as 2.267 g/mL, for silicon 2.3296 g/mL, and for boron 2.34 g/mL. If the device used to measure the density is accurate to +/- 0.1 then each of these elements would appear to have a density of 2.3 g/mL and we might conclude that all three have the same densities. But increase the accuracy to +/- 0.01 and carbon would be 2.27, silicon 2.33 and boron 2.34. Because density is not an exact value, eventually all substances would have different densities if you look with a high enough accuracy.

Greg (Roberto Gregorius) Canisius College


No, that is not correct. The density of liquid water is not unity; it changes depending on both the temperature and pressure -- you can change its density by 2%, from 0.995 to over 1.01 g/cm3.

Also, there are conceivably infinite compounds that fall within this range of densities, most notably organic liquids (benzonitrile, density of 1, comes to mind). In addition to heating/cooling or compressing, you can also adjust the density of substances by mixing them (adding ethanol to water lowers the density, while dissolving salts raise the density). In other words, there are many ways to get two materials to have equal density.

Hope this helps, Burr Zimmerman


You have a couple of misunderstandings about the density of substances:

The density of a substance is NOT unique. Density is the (mass / volume). So first of all it depends upon the temperature of the substance. It also depends upon the volume of the substance. This is small for solids and liquids, but not zero. It is very large for gases and vapors. The same substance can form more than a single crystal form. For those substances the density can be very different.

It is not true that "pure" water is the only known substance with a density of 1 gm / ml.

The density of a substance depends on the pressure applied to the substance. This pressure change can be very large. Amorphous substances such as polymers can vary in density over a wide range because they are pretty compressible.

Often density is defined as the (weight / volume). Although not rigorously true it is commonly used. Now the "weight" of a substance depends on even more variables -- for example, the force due gravity!! Mass and weight are not the same thing.

What has led you down the wrong path is the assumption that density is a unique property of a substance.

Vince Calder


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